#############################################################################
##
##  Exclude from testinstall.g as it takes considerable time.
##
gap> START_TEST("grpprmcs.tst");

# we don't want `DisplayCompositionSeries' to display the number of
# generators as this may differ, so we provide our own version of it.
gap> CustomDisplayCompositionSeries := function( S )
>   local   f,  i;
>   S := CompositionSeries( S );
>   Perform( S, Size );
>   Print( "Group\n" );
>   for i  in [2..Length(S)]  do
>     f:=Image(NaturalHomomorphismByNormalSubgroup(S[i-1],S[i]));
>     Print( " | ",IsomorphismTypeInfoFiniteSimpleGroup(f).name,"\n");
>     Print( "Group\n" );;
>   od;
> end;;

# missing (?):
# bbox
# dim8p3
# fi23.grp
# gl83.gen
# proba
# agl10.2
gap> g:=
> Group( (   1,   2)(   3,   4)(   5,   6)(   7,   8)(   9,  10)
> (  11,  12)(  13,  14)(  15,  16)(  17,  18)(  19,  20)(  21,  22)
> (  23,  24)(  25,  26)(  27,  28)(  29,  30)(  31,  32)(  33,  34)
> (  35,  36)(  37,  38)(  39,  40)(  41,  42)(  43,  44)(  45,  46)
> (  47,  48)(  49,  50)(  51,  52)(  53,  54)(  55,  56)(  57,  58)
> (  59,  60)(  61,  62)(  63,  64)(  65,  66)(  67,  68)(  69,  70)
> (  71,  72)(  73,  74)(  75,  76)(  77,  78)(  79,  80)(  81,  82)
> (  83,  84)(  85,  86)(  87,  88)(  89,  90)(  91,  92)(  93,  94)
> (  95,  96)(  97,  98)(  99, 100)( 101, 102)( 103, 104)( 105, 106)
> ( 107, 108)( 109, 110)( 111, 112)( 113, 114)( 115, 116)( 117, 118)
> ( 119, 120)( 121, 122)( 123, 124)( 125, 126)( 127, 128)( 129, 130)
> ( 131, 132)( 133, 134)( 135, 136)( 137, 138)( 139, 140)( 141, 142)
> ( 143, 144)( 145, 146)( 147, 148)( 149, 150)( 151, 152)( 153, 154)
> ( 155, 156)( 157, 158)( 159, 160)( 161, 162)( 163, 164)( 165, 166)
> ( 167, 168)( 169, 170)( 171, 172)( 173, 174)( 175, 176)( 177, 178)
> ( 179, 180)( 181, 182)( 183, 184)( 185, 186)( 187, 188)( 189, 190)
> ( 191, 192)( 193, 194)( 195, 196)( 197, 198)( 199, 200)( 201, 202)
> ( 203, 204)( 205, 206)( 207, 208)( 209, 210)( 211, 212)( 213, 214)
> ( 215, 216)( 217, 218)( 219, 220)( 221, 222)( 223, 224)( 225, 226)
> ( 227, 228)( 229, 230)( 231, 232)( 233, 234)( 235, 236)( 237, 238)
> ( 239, 240)( 241, 242)( 243, 244)( 245, 246)( 247, 248)( 249, 250)
> ( 251, 252)( 253, 254)( 255, 256)( 257, 258)( 259, 260)( 261, 262)
> ( 263, 264)( 265, 266)( 267, 268)( 269, 270)( 271, 272)( 273, 274)
> ( 275, 276)( 277, 278)( 279, 280)( 281, 282)( 283, 284)( 285, 286)
> ( 287, 288)( 289, 290)( 291, 292)( 293, 294)( 295, 296)( 297, 298)
> ( 299, 300)( 301, 302)( 303, 304)( 305, 306)( 307, 308)( 309, 310)
> ( 311, 312)( 313, 314)( 315, 316)( 317, 318)( 319, 320)( 321, 322)
> ( 323, 324)( 325, 326)( 327, 328)( 329, 330)( 331, 332)( 333, 334)
> ( 335, 336)( 337, 338)( 339, 340)( 341, 342)( 343, 344)( 345, 346)
> ( 347, 348)( 349, 350)( 351, 352)( 353, 354)( 355, 356)( 357, 358)
> ( 359, 360)( 361, 362)( 363, 364)( 365, 366)( 367, 368)( 369, 370)
> ( 371, 372)( 373, 374)( 375, 376)( 377, 378)( 379, 380)( 381, 382)
> ( 383, 384)( 385, 386)( 387, 388)( 389, 390)( 391, 392)( 393, 394)
> ( 395, 396)( 397, 398)( 399, 400)( 401, 402)( 403, 404)( 405, 406)
> ( 407, 408)( 409, 410)( 411, 412)( 413, 414)( 415, 416)( 417, 418)
> ( 419, 420)( 421, 422)( 423, 424)( 425, 426)( 427, 428)( 429, 430)
> ( 431, 432)( 433, 434)( 435, 436)( 437, 438)( 439, 440)( 441, 442)
> ( 443, 444)( 445, 446)( 447, 448)( 449, 450)( 451, 452)( 453, 454)
> ( 455, 456)( 457, 458)( 459, 460)( 461, 462)( 463, 464)( 465, 466)
> ( 467, 468)( 469, 470)( 471, 472)( 473, 474)( 475, 476)( 477, 478)
> ( 479, 480)( 481, 482)( 483, 484)( 485, 486)( 487, 488)( 489, 490)
> ( 491, 492)( 493, 494)( 495, 496)( 497, 498)( 499, 500)( 501, 502)
> ( 503, 504)( 505, 506)( 507, 508)( 509, 510)( 511, 512)( 513, 514)
> ( 515, 516)( 517, 518)( 519, 520)( 521, 522)( 523, 524)( 525, 526)
> ( 527, 528)( 529, 530)( 531, 532)( 533, 534)( 535, 536)( 537, 538)
> ( 539, 540)( 541, 542)( 543, 544)( 545, 546)( 547, 548)( 549, 550)
> ( 551, 552)( 553, 554)( 555, 556)( 557, 558)( 559, 560)( 561, 562)
> ( 563, 564)( 565, 566)( 567, 568)( 569, 570)( 571, 572)( 573, 574)
> ( 575, 576)( 577, 578)( 579, 580)( 581, 582)( 583, 584)( 585, 586)
> ( 587, 588)( 589, 590)( 591, 592)( 593, 594)( 595, 596)( 597, 598)
> ( 599, 600)( 601, 602)( 603, 604)( 605, 606)( 607, 608)( 609, 610)
> ( 611, 612)( 613, 614)( 615, 616)( 617, 618)( 619, 620)( 621, 622)
> ( 623, 624)( 625, 626)( 627, 628)( 629, 630)( 631, 632)( 633, 634)
> ( 635, 636)( 637, 638)( 639, 640)( 641, 642)( 643, 644)( 645, 646)
> ( 647, 648)( 649, 650)( 651, 652)( 653, 654)( 655, 656)( 657, 658)
> ( 659, 660)( 661, 662)( 663, 664)( 665, 666)( 667, 668)( 669, 670)
> ( 671, 672)( 673, 674)( 675, 676)( 677, 678)( 679, 680)( 681, 682)
> ( 683, 684)( 685, 686)( 687, 688)( 689, 690)( 691, 692)( 693, 694)
> ( 695, 696)( 697, 698)( 699, 700)( 701, 702)( 703, 704)( 705, 706)
> ( 707, 708)( 709, 710)( 711, 712)( 713, 714)( 715, 716)( 717, 718)
> ( 719, 720)( 721, 722)( 723, 724)( 725, 726)( 727, 728)( 729, 730)
> ( 731, 732)( 733, 734)( 735, 736)( 737, 738)( 739, 740)( 741, 742)
> ( 743, 744)( 745, 746)( 747, 748)( 749, 750)( 751, 752)( 753, 754)
> ( 755, 756)( 757, 758)( 759, 760)( 761, 762)( 763, 764)( 765, 766)
> ( 767, 768)( 769, 770)( 771, 772)( 773, 774)( 775, 776)( 777, 778)
> ( 779, 780)( 781, 782)( 783, 784)( 785, 786)( 787, 788)( 789, 790)
> ( 791, 792)( 793, 794)( 795, 796)( 797, 798)( 799, 800)( 801, 802)
> ( 803, 804)( 805, 806)( 807, 808)( 809, 810)( 811, 812)( 813, 814)
> ( 815, 816)( 817, 818)( 819, 820)( 821, 822)( 823, 824)( 825, 826)
> ( 827, 828)( 829, 830)( 831, 832)( 833, 834)( 835, 836)( 837, 838)
> ( 839, 840)( 841, 842)( 843, 844)( 845, 846)( 847, 848)( 849, 850)
> ( 851, 852)( 853, 854)( 855, 856)( 857, 858)( 859, 860)( 861, 862)
> ( 863, 864)( 865, 866)( 867, 868)( 869, 870)( 871, 872)( 873, 874)
> ( 875, 876)( 877, 878)( 879, 880)( 881, 882)( 883, 884)( 885, 886)
> ( 887, 888)( 889, 890)( 891, 892)( 893, 894)( 895, 896)( 897, 898)
> ( 899, 900)( 901, 902)( 903, 904)( 905, 906)( 907, 908)( 909, 910)
> ( 911, 912)( 913, 914)( 915, 916)( 917, 918)( 919, 920)( 921, 922)
> ( 923, 924)( 925, 926)( 927, 928)( 929, 930)( 931, 932)( 933, 934)
> ( 935, 936)( 937, 938)( 939, 940)( 941, 942)( 943, 944)( 945, 946)
> ( 947, 948)( 949, 950)( 951, 952)( 953, 954)( 955, 956)( 957, 958)
> ( 959, 960)( 961, 962)( 963, 964)( 965, 966)( 967, 968)( 969, 970)
> ( 971, 972)( 973, 974)( 975, 976)( 977, 978)( 979, 980)( 981, 982)
> ( 983, 984)( 985, 986)( 987, 988)( 989, 990)( 991, 992)( 993, 994)
> ( 995, 996)( 997, 998)( 999,1000)(1001,1002)(1003,1004)(1005,1006)
> (1007,1008)(1009,1010)(1011,1012)(1013,1014)(1015,1016)(1017,1018)
> (1019,1020)(1021,1022)(1023,1024), (257,513)(258,514)(259,515)(260,516)
> (261,517)(262,518)(263,519)(264,520)(265,521)(266,522)(267,523)
> (268,524)(269,525)(270,526)(271,527)(272,528)(273,529)(274,530)
> (275,531)(276,532)(277,533)(278,534)(279,535)(280,536)(281,537)
> (282,538)(283,539)(284,540)(285,541)(286,542)(287,543)(288,544)
> (289,545)(290,546)(291,547)(292,548)(293,549)(294,550)(295,551)
> (296,552)(297,553)(298,554)(299,555)(300,556)(301,557)(302,558)
> (303,559)(304,560)(305,561)(306,562)(307,563)(308,564)(309,565)
> (310,566)(311,567)(312,568)(313,569)(314,570)(315,571)(316,572)
> (317,573)(318,574)(319,575)(320,576)(321,577)(322,578)(323,579)
> (324,580)(325,581)(326,582)(327,583)(328,584)(329,585)(330,586)
> (331,587)(332,588)(333,589)(334,590)(335,591)(336,592)(337,593)
> (338,594)(339,595)(340,596)(341,597)(342,598)(343,599)(344,600)
> (345,601)(346,602)(347,603)(348,604)(349,605)(350,606)(351,607)
> (352,608)(353,609)(354,610)(355,611)(356,612)(357,613)(358,614)
> (359,615)(360,616)(361,617)(362,618)(363,619)(364,620)(365,621)
> (366,622)(367,623)(368,624)(369,625)(370,626)(371,627)(372,628)
> (373,629)(374,630)(375,631)(376,632)(377,633)(378,634)(379,635)
> (380,636)(381,637)(382,638)(383,639)(384,640)(385,641)(386,642)
> (387,643)(388,644)(389,645)(390,646)(391,647)(392,648)(393,649)
> (394,650)(395,651)(396,652)(397,653)(398,654)(399,655)(400,656)
> (401,657)(402,658)(403,659)(404,660)(405,661)(406,662)(407,663)
> (408,664)(409,665)(410,666)(411,667)(412,668)(413,669)(414,670)
> (415,671)(416,672)(417,673)(418,674)(419,675)(420,676)(421,677)
> (422,678)(423,679)(424,680)(425,681)(426,682)(427,683)(428,684)
> (429,685)(430,686)(431,687)(432,688)(433,689)(434,690)(435,691)
> (436,692)(437,693)(438,694)(439,695)(440,696)(441,697)(442,698)
> (443,699)(444,700)(445,701)(446,702)(447,703)(448,704)(449,705)
> (450,706)(451,707)(452,708)(453,709)(454,710)(455,711)(456,712)
> (457,713)(458,714)(459,715)(460,716)(461,717)(462,718)(463,719)
> (464,720)(465,721)(466,722)(467,723)(468,724)(469,725)(470,726)
> (471,727)(472,728)(473,729)(474,730)(475,731)(476,732)(477,733)
> (478,734)(479,735)(480,736)(481,737)(482,738)(483,739)(484,740)
> (485,741)(486,742)(487,743)(488,744)(489,745)(490,746)(491,747)
> (492,748)(493,749)(494,750)(495,751)(496,752)(497,753)(498,754)
> (499,755)(500,756)(501,757)(502,758)(503,759)(504,760)(505,761)
> (506,762)(507,763)(508,764)(509,765)(510,766)(511,767)(512,768), 
> (   2,   3,   5,   9,  17,  33,  65, 129, 257, 513)(   4,   7,  13,
>    25,  49,  97, 193, 385, 769, 514)(   6,  11,  21,  41,  81, 161,
>   321, 641, 258, 515)(   8,  15,  29,  57, 113, 225, 449, 897, 770, 516
>  )(  10,  19,  37,  73, 145, 289, 577, 130, 259, 517)(  12,  23,  45,
>    89, 177, 353, 705, 386, 771, 518)(  14,  27,  53, 105, 209, 417,
>   833, 642, 260, 519)(  16,  31,  61, 121, 241, 481, 961, 898, 772, 520
>  )(  18,  35,  69, 137, 273, 545,  66, 131, 261, 521)(  20,  39,  77,
>   153, 305, 609, 194, 387, 773, 522)(  22,  43,  85, 169, 337, 673,
>   322, 643, 262, 523)(  24,  47,  93, 185, 369, 737, 450, 899, 774, 524
>  )(  26,  51, 101, 201, 401, 801, 578, 132, 263, 525)(  28,  55, 109,
>   217, 433, 865, 706, 388, 775, 526)(  30,  59, 117, 233, 465, 929,
>   834, 644, 264, 527)(  32,  63, 125, 249, 497, 993, 962, 900, 776, 528
>  )(  34,  67, 133, 265, 529)(  36,  71, 141, 281, 561,  98, 195, 389,
>   777, 530)(  38,  75, 149, 297, 593, 162, 323, 645, 266, 531)
> (  40,  79, 157, 313, 625, 226, 451, 901, 778, 532)(  42,  83, 165,
>   329, 657, 290, 579, 134, 267, 533)(  44,  87, 173, 345, 689, 354,
>   707, 390, 779, 534)(  46,  91, 181, 361, 721, 418, 835, 646, 268, 535
>  )(  48,  95, 189, 377, 753, 482, 963, 902, 780, 536)(  50,  99, 197,
>   393, 785, 546,  68, 135, 269, 537)(  52, 103, 205, 409, 817, 610,
>   196, 391, 781, 538)(  54, 107, 213, 425, 849, 674, 324, 647, 270, 539
>  )(  56, 111, 221, 441, 881, 738, 452, 903, 782, 540)(  58, 115, 229,
>   457, 913, 802, 580, 136, 271, 541)(  60, 119, 237, 473, 945, 866,
>   708, 392, 783, 542)(  62, 123, 245, 489, 977, 930, 836, 648, 272, 543
>  )(  64, 127, 253, 505,1009, 994, 964, 904, 784, 544)(  70, 139, 277,
>   553,  82, 163, 325, 649, 274, 547)(  72, 143, 285, 569, 114, 227,
>   453, 905, 786, 548)(  74, 147, 293, 585, 146, 291, 581, 138, 275, 549
>  )(  76, 151, 301, 601, 178, 355, 709, 394, 787, 550)(  78, 155, 309,
>   617, 210, 419, 837, 650, 276, 551)(  80, 159, 317, 633, 242, 483,
>   965, 906, 788, 552)(  84, 167, 333, 665, 306, 611, 198, 395, 789, 554
>  )(  86, 171, 341, 681, 338, 675, 326, 651, 278, 555)(  88, 175, 349,
>   697, 370, 739, 454, 907, 790, 556)(  90, 179, 357, 713, 402, 803,
>   582, 140, 279, 557)(  92, 183, 365, 729, 434, 867, 710, 396, 791, 558
>  )(  94, 187, 373, 745, 466, 931, 838, 652, 280, 559)(  96, 191, 381,
>   761, 498, 995, 966, 908, 792, 560)( 100, 199, 397, 793, 562)
> ( 102, 203, 405, 809, 594, 164, 327, 653, 282, 563)( 104, 207, 413,
>   825, 626, 228, 455, 909, 794, 564)( 106, 211, 421, 841, 658, 292,
>   583, 142, 283, 565)( 108, 215, 429, 857, 690, 356, 711, 398, 795, 566
>  )( 110, 219, 437, 873, 722, 420, 839, 654, 284, 567)( 112, 223, 445,
>   889, 754, 484, 967, 910, 796, 568)( 116, 231, 461, 921, 818, 612,
>   200, 399, 797, 570)( 118, 235, 469, 937, 850, 676, 328, 655, 286, 571
>  )( 120, 239, 477, 953, 882, 740, 456, 911, 798, 572)( 122, 243, 485,
>   969, 914, 804, 584, 144, 287, 573)( 124, 247, 493, 985, 946, 868,
>   712, 400, 799, 574)( 126, 251, 501,1001, 978, 932, 840, 656, 288, 575
>  )( 128, 255, 509,1017,1010, 996, 968, 912, 800, 576)( 148, 295, 589,
>   154, 307, 613, 202, 403, 805, 586)( 150, 299, 597, 170, 339, 677,
>   330, 659, 294, 587)( 152, 303, 605, 186, 371, 741, 458, 915, 806, 588
>  )( 156, 311, 621, 218, 435, 869, 714, 404, 807, 590)( 158, 315, 629,
>   234, 467, 933, 842, 660, 296, 591)( 160, 319, 637, 250, 499, 997,
>   970, 916, 808, 592)( 166, 331, 661, 298, 595)( 168, 335, 669, 314,
>   627, 230, 459, 917, 810, 596)( 172, 343, 685, 346, 691, 358, 715,
>   406, 811, 598)( 174, 347, 693, 362, 723, 422, 843, 662, 300, 599)
> ( 176, 351, 701, 378, 755, 486, 971, 918, 812, 600)( 180, 359, 717,
>   410, 819, 614, 204, 407, 813, 602)( 182, 363, 725, 426, 851, 678,
>   332, 663, 302, 603)( 184, 367, 733, 442, 883, 742, 460, 919, 814, 604
>  )( 188, 375, 749, 474, 947, 870, 716, 408, 815, 606)( 190, 379, 757,
>   490, 979, 934, 844, 664, 304, 607)( 192, 383, 765, 506,1011, 998,
>   972, 920, 816, 608)( 206, 411, 821, 618, 212, 423, 845, 666, 308, 615
>  )( 208, 415, 829, 634, 244, 487, 973, 922, 820, 616)( 214, 427, 853,
>   682, 340, 679, 334, 667, 310, 619)( 216, 431, 861, 698, 372, 743,
>   462, 923, 822, 620)( 220, 439, 877, 730, 436, 871, 718, 412, 823, 622
>  )( 222, 443, 885, 746, 468, 935, 846, 668, 312, 623)( 224, 447, 893,
>   762, 500, 999, 974, 924, 824, 624)( 232, 463, 925, 826, 628)
> ( 236, 471, 941, 858, 692, 360, 719, 414, 827, 630)( 238, 475, 949,
>   874, 724, 424, 847, 670, 316, 631)( 240, 479, 957, 890, 756, 488,
>   975, 926, 828, 632)( 246, 491, 981, 938, 852, 680, 336, 671, 318, 635
>  )( 248, 495, 989, 954, 884, 744, 464, 927, 830, 636)( 252, 503,1005,
>   986, 948, 872, 720, 416, 831, 638)( 254, 507,1013,1002, 980, 936,
>   848, 672, 320, 639)( 256, 511,1021,1018,1012,1000, 976, 928, 832, 640
>  )( 342, 683)( 344, 687, 350, 699, 374, 747, 470, 939, 854, 684)
> ( 348, 695, 366, 731, 438, 875, 726, 428, 855, 686)( 352, 703, 382,
>   763, 502,1003, 982, 940, 856, 688)( 364, 727, 430, 859, 694)
> ( 368, 735, 446, 891, 758, 492, 983, 942, 860, 696)( 376, 751, 478,
>   955, 886, 748, 472, 943, 862, 700)( 380, 759, 494, 987, 950, 876,
>   728, 432, 863, 702)( 384, 767, 510,1019,1014,1004, 984, 944, 864, 704
>  )( 440, 879, 734, 444, 887, 750, 476, 951, 878, 732)( 448, 895, 766,
>   508,1015,1006, 988, 952, 880, 736)( 480, 959, 894, 764, 504,1007,
>   990, 956, 888, 752)( 496, 991, 958, 892, 760)( 512,1023,1022,1020,
>  1016,1008, 992, 960, 896, 768), ( 257, 769)( 258, 770)( 259, 771)
> ( 260, 772)( 261, 773)( 262, 774)( 263, 775)( 264, 776)( 265, 777)
> ( 266, 778)( 267, 779)( 268, 780)( 269, 781)( 270, 782)( 271, 783)
> ( 272, 784)( 273, 785)( 274, 786)( 275, 787)( 276, 788)( 277, 789)
> ( 278, 790)( 279, 791)( 280, 792)( 281, 793)( 282, 794)( 283, 795)
> ( 284, 796)( 285, 797)( 286, 798)( 287, 799)( 288, 800)( 289, 801)
> ( 290, 802)( 291, 803)( 292, 804)( 293, 805)( 294, 806)( 295, 807)
> ( 296, 808)( 297, 809)( 298, 810)( 299, 811)( 300, 812)( 301, 813)
> ( 302, 814)( 303, 815)( 304, 816)( 305, 817)( 306, 818)( 307, 819)
> ( 308, 820)( 309, 821)( 310, 822)( 311, 823)( 312, 824)( 313, 825)
> ( 314, 826)( 315, 827)( 316, 828)( 317, 829)( 318, 830)( 319, 831)
> ( 320, 832)( 321, 833)( 322, 834)( 323, 835)( 324, 836)( 325, 837)
> ( 326, 838)( 327, 839)( 328, 840)( 329, 841)( 330, 842)( 331, 843)
> ( 332, 844)( 333, 845)( 334, 846)( 335, 847)( 336, 848)( 337, 849)
> ( 338, 850)( 339, 851)( 340, 852)( 341, 853)( 342, 854)( 343, 855)
> ( 344, 856)( 345, 857)( 346, 858)( 347, 859)( 348, 860)( 349, 861)
> ( 350, 862)( 351, 863)( 352, 864)( 353, 865)( 354, 866)( 355, 867)
> ( 356, 868)( 357, 869)( 358, 870)( 359, 871)( 360, 872)( 361, 873)
> ( 362, 874)( 363, 875)( 364, 876)( 365, 877)( 366, 878)( 367, 879)
> ( 368, 880)( 369, 881)( 370, 882)( 371, 883)( 372, 884)( 373, 885)
> ( 374, 886)( 375, 887)( 376, 888)( 377, 889)( 378, 890)( 379, 891)
> ( 380, 892)( 381, 893)( 382, 894)( 383, 895)( 384, 896)( 385, 897)
> ( 386, 898)( 387, 899)( 388, 900)( 389, 901)( 390, 902)( 391, 903)
> ( 392, 904)( 393, 905)( 394, 906)( 395, 907)( 396, 908)( 397, 909)
> ( 398, 910)( 399, 911)( 400, 912)( 401, 913)( 402, 914)( 403, 915)
> ( 404, 916)( 405, 917)( 406, 918)( 407, 919)( 408, 920)( 409, 921)
> ( 410, 922)( 411, 923)( 412, 924)( 413, 925)( 414, 926)( 415, 927)
> ( 416, 928)( 417, 929)( 418, 930)( 419, 931)( 420, 932)( 421, 933)
> ( 422, 934)( 423, 935)( 424, 936)( 425, 937)( 426, 938)( 427, 939)
> ( 428, 940)( 429, 941)( 430, 942)( 431, 943)( 432, 944)( 433, 945)
> ( 434, 946)( 435, 947)( 436, 948)( 437, 949)( 438, 950)( 439, 951)
> ( 440, 952)( 441, 953)( 442, 954)( 443, 955)( 444, 956)( 445, 957)
> ( 446, 958)( 447, 959)( 448, 960)( 449, 961)( 450, 962)( 451, 963)
> ( 452, 964)( 453, 965)( 454, 966)( 455, 967)( 456, 968)( 457, 969)
> ( 458, 970)( 459, 971)( 460, 972)( 461, 973)( 462, 974)( 463, 975)
> ( 464, 976)( 465, 977)( 466, 978)( 467, 979)( 468, 980)( 469, 981)
> ( 470, 982)( 471, 983)( 472, 984)( 473, 985)( 474, 986)( 475, 987)
> ( 476, 988)( 477, 989)( 478, 990)( 479, 991)( 480, 992)( 481, 993)
> ( 482, 994)( 483, 995)( 484, 996)( 485, 997)( 486, 998)( 487, 999)
> ( 488,1000)( 489,1001)( 490,1002)( 491,1003)( 492,1004)( 493,1005)
> ( 494,1006)( 495,1007)( 496,1008)( 497,1009)( 498,1010)( 499,1011)
> ( 500,1012)( 501,1013)( 502,1014)( 503,1015)( 504,1016)( 505,1017)
> ( 506,1018)( 507,1019)( 508,1020)( 509,1021)( 510,1022)( 511,1023)
> ( 512,1024) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | A(9,2) = L(10,2) 
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 375234700595146883504949480652800, 1024, 1 ]

# agl1103.gen
gap> perm1:= PermList( Concatenation( [ 2 .. 1103 ], [ 1 ] ) );;
gap> perm2:= PermList( List( [1 .. 1103 ], x -> (5*x mod 1103) +1 ) );;
gap> g:= Group( perm1, perm2 );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Z(2)
Group
 | Z(19)
Group
 | Z(29)
Group
 | Z(1103)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 1215506, 607753, 31987, 1103, 1 ]

# $Co_2$ on 2300 points
gap> g:=
> Group( (   1,   4)(   2,   7)(   5,  10)(   6,  12)(   8,  17)
> (  11,  18)(  13,  24)(  15,  25)(  16,  23)(  20,  30)(  21,  31)
> (  22,  33)(  26,  42)(  27,  45)(  28,  40)(  29,  41)(  34,  46)
> (  36,  60)(  37,  63)(  38,  52)(  43,  72)(  47,  49)(  48,  80)
> (  50,  84)(  51,  87)(  53,  69)(  54,  76)(  56,  77)(  57,  78)
> (  58, 104)(  59, 106)(  61, 109)(  62, 110)(  64, 116)(  65, 117)
> (  67,  82)(  68, 124)(  71, 129)(  73, 131)(  74,  90)(  79, 142)
> (  81, 146)(  83, 148)(  85, 151)(  86, 152)(  88, 155)(  89, 156)
> (  91, 126)(  92, 159)(  93, 164)(  94, 136)(  95, 137)(  97, 138)
> (  98, 171)( 100, 140)( 101, 141)( 103, 128)( 107, 178)( 108, 179)
> ( 111, 183)( 112, 193)( 113, 186)( 114, 187)( 115, 199)( 118, 201)
> ( 119, 204)( 120, 209)( 121, 130)( 122, 165)( 123, 215)( 125, 219)
> ( 127, 132)( 133, 224)( 134, 135)( 139, 228)( 143, 232)( 144, 233)
> ( 147, 241)( 149, 243)( 150, 244)( 153, 250)( 154, 251)( 157, 258)
> ( 158, 259)( 160, 265)( 161, 246)( 162, 264)( 163, 225)( 166, 271)
> ( 167, 276)( 168, 277)( 169, 279)( 170, 227)( 172, 281)( 173, 284)
> ( 175, 222)( 180, 290)( 181, 295)( 182, 296)( 184, 303)( 185, 292)
> ( 188, 312)( 189, 298)( 190, 317)( 191, 301)( 192, 320)( 194, 321)
> ( 195, 324)( 196, 309)( 197, 328)( 198, 332)( 200, 334)( 202, 256)
> ( 205, 345)( 206, 335)( 207, 338)( 208, 349)( 210, 351)( 211, 223)
> ( 212, 269)( 213, 273)( 214, 216)( 217, 357)( 218, 356)( 220, 364)
> ( 221, 366)( 226, 280)( 229, 370)( 230, 371)( 234, 375)( 235, 380)
> ( 236, 381)( 238, 272)( 240, 388)( 242, 392)( 245, 291)( 247, 395)
> ( 248, 336)( 249, 257)( 252, 260)( 253, 405)( 254, 310)( 255, 267)
> ( 261, 414)( 262, 409)( 263, 416)( 266, 419)( 268, 421)( 270, 353)
> ( 274, 352)( 275, 427)( 278, 430)( 282, 434)( 283, 385)( 285, 439)
> ( 287, 358)( 289, 443)( 293, 447)( 294, 450)( 297, 453)( 299, 456)
> ( 300, 444)( 302, 462)( 304, 455)( 305, 464)( 306, 468)( 307, 446)
> ( 308, 472)( 311, 477)( 313, 480)( 314, 481)( 315, 454)( 316, 486)
> ( 318, 487)( 319, 488)( 322, 491)( 323, 494)( 325, 497)( 326, 498)
> ( 327, 425)( 329, 501)( 330, 502)( 331, 504)( 333, 507)( 339, 399)
> ( 340, 517)( 341, 406)( 342, 523)( 344, 527)( 346, 530)( 347, 531)
> ( 348, 536)( 350, 539)( 354, 544)( 355, 359)( 360, 547)( 361, 545)
> ( 362, 436)( 363, 551)( 365, 555)( 367, 557)( 368, 433)( 369, 432)
> ( 376, 461)( 377, 393)( 378, 572)( 379, 575)( 383, 580)( 386, 583)
> ( 387, 586)( 389, 590)( 390, 591)( 391, 576)( 394, 600)( 396, 511)
> ( 397, 516)( 398, 512)( 400, 407)( 401, 607)( 402, 411)( 403, 412)
> ( 404, 413)( 408, 615)( 410, 619)( 415, 629)( 417, 435)( 420, 632)
> ( 422, 633)( 423, 634)( 424, 637)( 426, 639)( 428, 429)( 431, 642)
> ( 437, 649)( 438, 651)( 440, 654)( 445, 570)( 448, 663)( 449, 664)
> ( 451, 638)( 452, 656)( 457, 674)( 458, 657)( 459, 658)( 460, 680)
> ( 463, 617)( 465, 673)( 466, 685)( 467, 690)( 469, 693)( 470, 695)
> ( 471, 697)( 473, 701)( 474, 702)( 475, 705)( 476, 618)( 478, 711)
> ( 479, 712)( 482, 716)( 483, 727)( 484, 719)( 485, 720)( 489, 736)
> ( 490, 738)( 492, 742)( 493, 743)( 495, 746)( 496, 744)( 499, 753)
> ( 500, 754)( 503, 755)( 505, 758)( 506, 757)( 509, 672)( 515, 773)
> ( 518, 520)( 519, 777)( 521, 781)( 522, 784)( 524, 786)( 525, 789)
> ( 526, 791)( 528, 795)( 529, 796)( 532, 799)( 533, 810)( 534, 802)
> ( 535, 803)( 537, 816)( 538, 614)( 542, 825)( 543, 826)( 546, 828)
> ( 548, 648)( 549, 831)( 550, 834)( 552, 838)( 553, 839)( 554, 827)
> ( 558, 847)( 559, 647)( 560, 643)( 561, 644)( 567, 683)( 571, 599)
> ( 573, 574)( 578, 865)( 581, 869)( 582, 871)( 584, 873)( 585, 876)
> ( 587, 588)( 589, 878)( 592, 884)( 593, 892)( 594, 886)( 595, 887)
> ( 596, 861)( 597, 862)( 598, 820)( 601, 602)( 603, 829)( 604, 776)
> ( 605, 904)( 606, 907)( 608, 902)( 609, 623)( 610, 624)( 611, 625)
> ( 612, 916)( 613, 627)( 616, 860)( 620, 925)( 621, 761)( 622, 710)
> ( 626, 934)( 628, 815)( 631, 739)( 635, 942)( 636, 944)( 640, 641)
> ( 645, 950)( 650, 955)( 652, 956)( 653, 957)( 659, 676)( 660, 858)
> ( 661, 969)( 665, 972)( 666, 981)( 667, 975)( 668, 976)( 669, 965)
> ( 670, 947)( 675, 966)( 677, 849)( 678, 848)( 679, 998)( 681,1001)
> ( 682,1002)( 684, 752)( 686,1009)( 687,1012)( 689,1016)( 691,1020)
> ( 692,1021)( 694,1027)( 696, 983)( 698,1032)( 699,1034)( 700,1031)
> ( 703,1043)( 704,1048)( 706,1050)( 707,1051)( 708, 918)( 709, 924)
> ( 713,1060)( 714,1065)( 715, 730)( 717,1072)( 718, 974)( 722,1066)
> ( 723,1082)( 724,1068)( 725,1070)( 726,1089)( 728,1094)( 729,1093)
> ( 731,1076)( 732,1102)( 734, 745)( 735, 741)( 737,1033)( 740,1112)
> ( 747,1121)( 748,1122)( 749,1019)( 750,1123)( 751, 763)( 756,1140)
> ( 759,1141)( 760,1142)( 762,1143)( 765,1158)( 766, 993)( 772,1167)
> ( 774,1170)( 775,1171)( 778,1144)( 779,1176)( 780,1179)( 782,1182)
> ( 783,1183)( 785, 787)( 788,1189)( 790, 812)( 792,1194)( 793,1195)
> ( 794,1193)( 797,1204)( 798,1208)( 800,1215)( 805,1209)( 806,1221)
> ( 807,1211)( 808,1213)( 809,1225)( 811,1228)( 813,1218)( 814,1197)
> ( 817, 920)( 818, 921)( 819,1181)( 823,1245)( 832,1255)( 833,1256)
> ( 835,1261)( 836,1262)( 837,1260)( 840,1266)( 841,1269)( 842, 843)
> ( 844,1254)( 846,1113)( 850,1279)( 855,1285)( 856,1287)( 859, 897)
> ( 863,1293)( 866,1296)( 867,1298)( 868,1295)( 870,1303)( 872, 874)
> ( 875,1249)( 877, 881)( 879, 883)( 880,1313)( 882, 894)( 885,1316)
> ( 888,1315)( 889,1318)( 890, 891)( 893,1321)( 895,1267)( 896,1322)
> ( 898,1292)( 899,1240)( 900,1328)( 901,1331)( 903,1251)( 905,1333)
> ( 906,1332)( 908,1237)( 909,1336)( 910,1320)( 911,1338)( 912, 931)
> ( 913,1340)( 914,1341)( 915,1342)( 917,1344)( 919,1348)( 922,1290)
> ( 923,1351)( 926,1353)( 927,1150)( 928,1151)( 929,1058)( 930,1059)
> ( 932,1358)( 933,1359)( 935,1362)( 936,1235)( 937,1236)( 938,1365)
> ( 939,1368)( 940,1115)( 941,1276)( 943,1374)( 945,1375)( 946, 990)
> ( 948,1120)( 949,1378)( 951,1379)( 954,1250)( 958,1384)( 959,1393)
> ( 960,1387)( 961,1388)( 962,1396)( 967, 968)( 973,1414)( 977,1408)
> ( 978,1410)( 979,1412)( 980,1422)( 982,1425)( 984,1418)( 985,1430)
> ( 986,1399)( 987,1392)( 988,1302)( 992,1441)( 994,1445)( 995,1278)
> ( 996,1446)( 997,1447)( 999,1169)(1000,1168)(1003,1452)(1004,1456)
> (1005,1454)(1006,1137)(1007,1138)(1008,1458)(1010,1461)(1011,1462)
> (1013,1467)(1014,1468)(1015,1470)(1017,1474)(1018,1475)(1022,1419)
> (1023,1428)(1024,1481)(1025,1482)(1026,1490)(1028,1493)(1029,1494)
> (1030,1466)(1035,1501)(1036,1512)(1037,1513)(1038,1504)(1039,1507)
> (1040,1498)(1041,1499)(1042,1500)(1044,1485)(1045,1523)(1046,1486)
> (1047,1457)(1049,1527)(1052,1528)(1053,1532)(1054,1530)(1055,1531)
> (1056,1086)(1057,1539)(1061,1548)(1062,1545)(1063,1547)(1064,1550)
> (1067,1556)(1069,1411)(1071,1559)(1073,1564)(1074,1563)(1075,1565)
> (1077,1571)(1079,1553)(1080,1555)(1081,1576)(1083,1579)(1084,1581)
> (1085,1557)(1087,1584)(1088,1587)(1090,1591)(1091,1590)(1092,1593)
> (1095,1360)(1096,1598)(1097,1596)(1098,1319)(1099,1600)(1100,1568)
> (1101,1603)(1103,1104)(1105,1116)(1106,1117)(1107,1119)(1108,1139)
> (1109,1505)(1110,1506)(1111,1126)(1114,1611)(1118,1460)(1124,1273)
> (1125,1618)(1127,1131)(1128,1613)(1129,1614)(1130,1311)(1132,1478)
> (1133,1479)(1134,1602)(1135,1636)(1136,1639)(1146,1645)(1147,1646)
> (1148,1324)(1149,1650)(1152,1196)(1153,1655)(1154,1656)(1156,1659)
> (1157,1663)(1159,1665)(1160,1443)(1161,1669)(1162,1670)(1164,1633)
> (1165,1671)(1166,1449)(1172,1536)(1173,1519)(1174,1647)(1175,1217)
> (1177,1524)(1178,1678)(1180,1680)(1184,1683)(1185,1364)(1186,1688)
> (1187,1690)(1188,1691)(1190,1693)(1191,1694)(1192,1677)(1198,1701)
> (1199,1205)(1200,1543)(1201,1697)(1202,1203)(1206,1708)(1207,1709)
> (1210,1712)(1214,1714)(1216,1716)(1220,1401)(1222,1719)(1223,1721)
> (1224,1713)(1226,1722)(1227,1720)(1229,1724)(1230,1727)(1231,1728)
> (1232,1699)(1233,1717)(1234,1700)(1238,1732)(1239,1681)(1241,1735)
> (1242,1682)(1244,1736)(1246,1738)(1248,1742)(1257,1747)(1258,1617)
> (1259,1749)(1263,1753)(1264,1756)(1265,1752)(1268,1757)(1270,1642)
> (1271,1746)(1272,1381)(1274,1275)(1277,1758)(1281,1759)(1284,1761)
> (1286,1763)(1288,1766)(1289,1767)(1291,1770)(1294,1433)(1297,1773)
> (1299,1300)(1301,1771)(1304,1407)(1305,1403)(1306,1687)(1307,1755)
> (1308,1776)(1309,1310)(1312,1782)(1314,1785)(1317,1786)(1323,1787)
> (1325,1788)(1326,1790)(1327,1791)(1329,1793)(1330,1794)(1334,1797)
> (1335,1540)(1337,1651)(1339,1626)(1343,1784)(1345,1804)(1346,1805)
> (1347,1806)(1349,1808)(1350,1809)(1352,1811)(1354,1814)(1355,1815)
> (1356,1816)(1357,1817)(1361,1820)(1363,1821)(1366,1824)(1367,1825)
> (1369,1432)(1370,1826)(1371,1823)(1372,1827)(1373,1605)(1376,1607)
> (1377,1437)(1380,1829)(1382,1644)(1385,1772)(1389,1836)(1390,1777)
> (1391,1832)(1394,1838)(1395,1840)(1400,1779)(1406,1854)(1409,1597)
> (1413,1862)(1415,1867)(1416,1866)(1417,1871)(1420,1453)(1421,1875)
> (1423,1879)(1424,1580)(1426,1883)(1427,1884)(1429,1873)(1431,1455)
> (1434,1775)(1436,1890)(1439,1896)(1440,1899)(1442,1739)(1444,1905)
> (1448,1535)(1450,1492)(1451,1673)(1459,1910)(1463,1911)(1464,1914)
> (1465,1915)(1469,1916)(1471,1921)(1472,1922)(1473,1765)(1476,1926)
> (1477,1929)(1480,1641)(1483,1919)(1484,1723)(1487,1939)(1488,1934)
> (1489,1940)(1491,1941)(1495,1943)(1496,1948)(1497,1946)(1502,1511)
> (1503,1958)(1508,1947)(1509,1953)(1510,1715)(1514,1963)(1515,1949)
> (1516,1965)(1517,1951)(1518,1818)(1520,1674)(1521,1952)(1522,1972)
> (1525,1974)(1526,1970)(1529,1977)(1533,1609)(1534,1898)(1537,1583)
> (1538,1979)(1541,1981)(1542,1913)(1544,1982)(1546,1975)(1549,1984)
> (1551,1679)(1554,1857)(1558,1989)(1560,1994)(1561,1993)(1562,1938)
> (1566,1996)(1567,1997)(1570,1998)(1572,1999)(1573,1734)(1574,2000)
> (1575,1582)(1577,2002)(1578,2004)(1585,1942)(1586,2010)(1588,2011)
> (1589,1594)(1592,1961)(1595,2021)(1599,1819)(1601,1606)(1604,1638)
> (1608,1908)(1610,1643)(1612,2034)(1615,2036)(1616,1628)(1619,2008)
> (1620,2045)(1621,2042)(1622,2050)(1623,1631)(1624,1632)(1625,2055)
> (1627,1780)(1629,2059)(1630,2063)(1634,1930)(1635,1931)(1637,2072)
> (1640,2076)(1649,2077)(1652,2079)(1653,1945)(1654,2080)(1657,2081)
> (1658,2082)(1660,2084)(1661,2086)(1662,1705)(1664,2087)(1666,2085)
> (1667,1902)(1668,1903)(1675,1845)(1676,1686)(1684,1703)(1685,2092)
> (1689,1955)(1692,2096)(1695,2043)(1696,2091)(1698,1933)(1702,2099)
> (1704,2100)(1706,2101)(1707,2102)(1711,2103)(1725,2107)(1726,2030)
> (1729,1987)(1730,1874)(1731,2093)(1733,1894)(1737,2111)(1744,2115)
> (1748,2037)(1750,2039)(1751,2117)(1754,2122)(1760,2126)(1764,2129)
> (1768,1886)(1769,2132)(1774,2133)(1778,1852)(1781,2134)(1783,2135)
> (1789,2016)(1792,2137)(1795,1799)(1796,1928)(1798,2139)(1800,1976)
> (1801,2125)(1802,1851)(1803,2024)(1807,1980)(1810,1950)(1812,2114)
> (1813,1920)(1822,2146)(1830,2152)(1831,2105)(1834,2136)(1835,2163)
> (1839,1846)(1841,1859)(1844,2168)(1849,2170)(1853,2173)(1855,2175)
> (1856,2179)(1858,2025)(1860,2184)(1861,2071)(1863,1868)(1864,2067)
> (1865,2176)(1869,2171)(1870,2195)(1872,2073)(1876,2199)(1877,2165)
> (1878,2003)(1880,2196)(1881,2006)(1882,2007)(1885,2119)(1888,2121)
> (1889,2213)(1891,2142)(1892,2141)(1893,2215)(1895,2144)(1897,2161)
> (1900,2218)(1901,2220)(1904,2150)(1906,2217)(1907,2029)(1909,1924)
> (1912,2147)(1917,2018)(1918,1959)(1923,2130)(1925,1995)(1927,2145)
> (1932,2191)(1935,2204)(1936,1957)(1937,2178)(1944,2224)(1954,2222)
> (1956,2223)(1960,2233)(1962,2118)(1964,1967)(1966,2185)(1968,2237)
> (1969,2090)(1971,2239)(1973,1986)(1978,2031)(1983,2019)(1985,2221)
> (1988,2032)(1990,2026)(1991,2028)(1992,2227)(2001,2154)(2005,2253)
> (2009,2022)(2012,2097)(2013,2151)(2014,2015)(2017,2023)(2020,2225)
> (2027,2075)(2033,2180)(2035,2260)(2038,2058)(2040,2263)(2041,2206)
> (2044,2047)(2046,2203)(2048,2054)(2049,2265)(2051,2198)(2052,2066)
> (2053,2188)(2056,2194)(2057,2269)(2060,2274)(2061,2201)(2062,2249)
> (2064,2271)(2065,2200)(2068,2162)(2069,2259)(2070,2229)(2074,2192)
> (2078,2261)(2083,2284)(2088,2283)(2098,2286)(2104,2110)(2106,2109)
> (2108,2287)(2112,2235)(2113,2276)(2116,2242)(2120,2252)(2123,2143)
> (2124,2254)(2138,2140)(2148,2228)(2149,2244)(2153,2278)(2155,2226)
> (2158,2257)(2159,2246)(2160,2258)(2166,2183)(2167,2181)(2169,2255)
> (2172,2272)(2174,2294)(2177,2197)(2182,2211)(2186,2281)(2187,2264)
> (2189,2193)(2190,2298)(2202,2238)(2205,2256)(2207,2266)(2208,2216)
> (2209,2299)(2210,2289)(2212,2268)(2214,2295)(2219,2290)(2230,2292)
> (2231,2241)(2232,2240)(2234,2248)(2236,2262)(2243,2247)(2245,2282)
> (2250,2277)(2267,2273)(2270,2279)(2275,2280)(2288,2297)(2291,2293)
> (2296,2300), (   2,  21,  26,  27,  11,  22,  39,  15,   5,   3,   8,
>    13,  14,   6,   9)(   4,  20, 208,  81,  28,  23,  76, 331, 114,
>   223, 222, 278, 559, 194,  19)(   7,  79, 154,  90,  69,  70, 268,
>   426, 224,  71, 128, 163, 359,  82,  16)(  10,  36,  95, 215, 648,
>   175, 164, 282, 245, 638, 211, 169, 140, 118,  89)(  12,  83, 423,
>   273, 168,  33,  34, 195, 352, 121, 127, 286, 546, 283,  72)
> (  17,  48, 147, 365, 196,  53,  54, 424, 943, 431, 134,  98, 102, 210,
>  65)(  18,  37,  52,  85, 229,  25,  68, 451, 358, 263,  47,  50, 227,
>   180, 172)(  24, 123, 220, 197,  35, 104, 105, 198, 367, 126,  74,
>    97, 323, 113, 135)(  29,  30, 261, 489, 264,  67,  51,  66, 297,
>   108, 103, 212, 542, 503, 207)(  31, 221, 558, 492, 191, 133,  56,
>   322, 499, 217,  40,  93, 174, 440, 173)(  32,  55,  94, 437, 353,
>   132,  43,  46, 253, 119,  41,  44, 159, 354, 157)(  38,  64,  86,
>    77, 348, 125, 269, 501, 235, 236, 153, 189, 137, 112, 115)
> (  42, 160, 255,  49,  73)(  45, 122, 158, 295, 262,  91,  92, 141,
>   111, 166,  96, 167, 100, 161, 230)(  57, 107, 355, 441, 636, 271,
>   192, 254, 421, 422, 318, 139,  78,  88, 120)(  58,  59, 288, 190,
>   315,  75, 226, 274, 379, 425, 129, 214, 655, 356, 329)
> (  60, 401,1495,1674, 459, 376, 378,1307,1427, 307, 248, 252, 812,1486,
>  305)(  61, 162, 136, 326, 213, 143, 328, 234, 420, 267, 206, 170, 181,
>  182, 177)(  62,  99, 225, 543, 635, 436, 130, 176, 330, 537, 150, 131,
>  287, 289, 200)(  63, 408,1463, 603, 407, 299, 646,1112,1122, 569, 486,
>  1294,1055,1364, 341)(  80, 582,1298,1687, 579, 556, 846,1263,1083,
>   433, 643, 949,1140,1273, 362)(  84, 308,1025,1780, 857, 279, 460,
>  1487, 811, 117, 257, 694,1167,1750, 406)(  87, 344,1702,1699, 776,
>   256, 260, 730, 896, 219, 372, 585, 745,1538, 398)( 101, 272, 275,
>   138, 319, 368, 294, 415, 450, 500, 357, 545, 442, 165, 285)
> ( 106, 311, 627,1345, 673, 659,1233, 797, 814, 204, 399, 838,1335,1350,
>  310)( 109, 605, 902, 842, 463, 366, 867, 960,1575, 849, 675, 884, 484,
>  883, 599)( 110, 249, 778, 936,1675, 371, 145, 240, 586, 893, 858, 184,
>  188, 591, 729)( 116, 606, 860,1798, 787, 683, 757,1113, 980, 581, 577,
>  850,1115,1585, 524)( 124, 830,1764,1363, 617, 570, 687, 667, 723, 561,
>  575, 855,1314, 897, 239)( 142, 856,1038,1049, 995, 291, 293, 983, 726,
>  693, 151, 467,1451,1534, 309)( 144, 149, 417, 505, 325, 270, 316, 493,
>  756, 650, 327, 216, 360, 242, 350)( 146, 383,1672,1054, 919, 251, 510,
>  870, 961, 889, 660, 513, 772,1088, 894)( 148, 438,1079,1760, 848, 733,
>  948, 532,1644, 629, 361, 549, 395,1272, 410)( 152, 185, 598, 572, 878,
>  374, 377,1141,1465,1208, 512, 369, 825,1259, 914)( 155, 521,1537,1308,
>  384, 238, 402, 485,1116, 968, 183, 737,1379,1098, 446)( 156, 203,1187,
>  937, 844, 244, 428,1166,1257, 744, 639, 863,1162, 873, 933)
> ( 171, 515,1184,1686, 518, 462, 618,1270, 945, 427, 300, 994, 611, 806,
>  644)( 178, 476,1535,1696, 568, 455,1315, 703,1907, 678, 298, 734,1035,
>  1526, 469)( 179, 292, 555,1022,1489, 466, 418, 504,1327,1514, 465,
>   458,1266,1469, 982)( 186, 397, 590, 998,1789, 620, 218, 363,1395,
>  1876, 688, 456, 634,1003, 985)( 187, 445,1080,1283,1390, 864, 228,
>   490, 921, 596, 233, 373, 621, 910, 732)( 193, 526, 535,1700, 685,
>   468, 392,1349,1276, 434, 567, 387, 595,1578, 630)( 199, 509,1664,
>  1235,1685,1202,1698,1218, 820, 821,1697,2088,1158,1652,1074)
> ( 201, 686, 494,1781, 866, 276, 475, 922,1726, 771, 382, 939, 742,1047,
>  770)( 202, 205, 839,1455, 786, 336, 562, 544,1430, 777, 339,1026, 592,
>  1450, 514)( 209, 541,1737, 781,1332,1572, 752,1145,1654, 803,1566,
>  1067,1378,1171,1216)( 231, 411,1476,1431, 457, 432, 645, 665,1783,
>   565, 564, 754,1768,2116, 548)( 232, 926,1778, 898, 619, 317, 471,
>   668,1064, 464, 280, 997,1005, 903, 520)( 237, 386, 381, 900, 785,
>   511, 622, 613,1046,1163, 966, 885, 625, 728, 768)( 241,1091, 930,
>   616,1347,1143, 739,1292,1011, 746,1121,1370, 491,1053,1056)
> ( 243, 563, 874,1394, 284, 444,1401,1280,1118, 487, 306, 661, 840, 862,
>  604)( 246, 247, 495, 333, 266)( 250, 304, 996, 931,1533, 454, 380,
>  1352,1196,1207, 925, 303, 435,1052,1330)( 258, 340,1164, 713,1291)
> ( 259, 396, 938, 847,1268, 674, 430,1277, 958,1536, 338, 461, 502, 920,
>  935)( 265,1015,1039, 892, 658, 676, 679,1024,1376, 370, 320, 689,1745,
>  1613, 845)( 277, 429,1302,1845,1301)( 281, 337, 779, 534, 917, 571,
>   523, 788,1316, 576, 400, 517,1173,1464,1119)( 290, 394, 881,1602,
>   419, 566, 684, 637, 915, 677, 375,1008,1199,1206,1278)
> ( 296, 990,2214,1948,1916,1548,1807,2064,2189,2172,2190,1634,1454,1633,
>  1416)( 301, 302, 631,1743,1457)( 312, 796,1704,1183,1570,1138, 773,
>   538, 527,1336,1711,1441,2083,1666, 508)( 313, 859, 602,1252,2098,
>  1300, 871,1306,1305,1304,1081,1367, 951, 666, 449)( 314, 573,1312,
>  1253, 832, 554, 615,1017,2090,1391,1085,1284, 978,1377, 483)
> ( 321, 342, 525,1337,1339, 409, 522,1186,1324,1371, 557, 578, 946, 482,
>  1612)( 324,1629,1351,1895,1012,2011,1027,1619,1656,2270,1128,2043,
>  2218,2081,1419)( 332,1214,1560,1152,1667,1552,1531,1213,1203, 824,
>  1150,1733, 498,1681,1077)( 334, 765, 711,1540,1333,1058,1573,1076,
>  1574, 720,1543,1549,1741,1060,1161)( 335, 550, 594,1095, 640, 560,
>   875,1605,1231, 343, 516, 780, 600,1751,1165)( 345, 712,1542,1181,
>  1201,1657,1658,1156,1157,1683,1210,1279,1051,1653, 540)
> ( 346, 901, 574, 583, 391, 607,1180, 837, 624,1010, 741, 950,1086, 626,
>  404)( 347, 601,1614,1249, 547,1271, 628, 551,1356,1357, 891,1084, 852,
>  1373, 533)( 349,1649, 760, 761,1713,1899,1710,1247,1061, 719,1147,
>  1643, 753,1641,1194)( 351, 823, 795, 904,1796, 791, 815,1139, 762,
>   763,1195,1706,1211,1212,1248)( 364,1023,1014, 969, 841, 390, 880,
>  1599, 653, 774,1185,1178, 789,1355,1317)( 385, 393, 470,1497,1323)
> ( 388,1030, 474,1037, 612, 413, 448,1426, 775,1174,1676,1484,1488,1334,
>  614)( 389, 861, 836)( 403,1230, 682,1006,1250, 633,1288,1512,1646,
>  1812,1197,1191, 979, 879, 833)( 405,1326,1423, 872,1392,1582, 977,
>   984,1117, 807, 942,1004,1000, 927, 911)( 412, 882, 707, 918, 843,
>   909, 609,1099,1063,1290,1281, 724,1274,1264, 584)( 414, 908,1226,
>   888, 731, 913, 886, 725,1577, 940,1309,1361, 743, 706, 923)
> ( 416, 784,1188,1200, 809, 967, 769,1429,1282,1222, 642, 767,1297,1310,
>  827)( 439, 964, 974,1860,2275,2154,2156,2261,1790, 727,1998,2271,2252,
>  2253, 986)( 443, 641, 580,1393,1399,2126,1771,1293,1772,1846,1838,
>  1296, 868, 947, 656)( 447,1261,2139,1820,2106,1961,2280,1840,1827,
>   831,2040,1787,2241,1900, 671)( 452, 672,1901,1989,2258,1985,1639,
>  1694,1527,1986,2109,1506,1127,2004,1844)( 453,1436,1262,2119,2027,
>  1102,1926,1382,1383,2289,1824,1624,1621,1019,1444)( 472, 810,1786,
>  2124,1637,1930,1842,2283,1973,2092,2185,1130,1135,1408, 496)
> ( 473,1885,1586, 792,1232,1045,1673,1258, 588, 552,1421,1472, 899, 589,
>  610)( 477,1541,1544,1068,1069, 717, 721, 481, 801,1703,1182, 907,1731,
>  1238, 506)( 478,1057, 890, 695,1329,1459,1645,1234,1509,1190,1318,
>   479, 608,1496, 699)( 480,1242,1170, 536,2093,1237, 822,1561,2000,
>  1567,1740,1553,1554, 716,1075)( 488,2031,1880,2045,2067,2068,2177,
>  1850,2018,1595,2010,1475,1021,1132,1452)( 497,1131,2071, 747,2078,
>  1941,2017,2046,1340,1912,1655,1413,2117,1106,1136)( 507,1149,1240,
>   759,1209,1528,1529,1070,1059, 766,2086,2082,1155,1236,1154)
> ( 519, 657,1100, 912,1729)( 528,1709,1692,1511,1251,1110, 632,1325,
>  1018, 877,1111,1275,1471,1695, 793)( 529,1198,1708,1510,1177,1223,
>   953, 738,1744,1286, 587,1097, 924,1028,1192)( 530,1151,1050,1243,
>  1680, 710,1078,1990,1148,1153,1066,1988,1545, 799,1217)
> ( 531, 718,1682,1684,1647,1179, 705,1239,1244,1193,1707,1668,1204, 800,
>  804)( 539,1241,1734, 817,1976,1555,1547,1160,1205, 802,1073,1648,1718,
>  1137,1144)( 553, 835,1319, 709, 851, 829,1104, 929,1346,1267,1142,
>  1114, 758,1491, 593)( 597, 906, 623,1477,1354,1366, 941, 740,1013,
>  1096, 854, 652,1172,1169,1689)( 647, 681,1679, 783, 853,1776,1775,
>  2089,1229, 805,1320, 704, 696,1109,1380)( 649,1630,2230,1805,1439,
>  1440,1518,2053,2001,1611,1747,2016,1598,2121,1834)( 651,1403, 955,
>  1628,2298,2033, 972,1342,1891,1331,1255,2054,2074, 973, 963)
> ( 654, 664,1407,2024,1285,1753,2057,2266,2237,2206,1550,2240,1502,1508,
>  1406)( 662, 702,1520,2097,1996,2153,1931,2292,2229,1794,2262,2300,
>  2183,2138, 989)( 663,2120,1365,2003,1626,1978,2164, 957,1386,2163,
>  2061,1338,1381,2142,1417)( 669,1832,1833,1432,1792,1588,1093,1715,
>  1460,2222,1815,1438,2030,1607,1831)( 670, 992, 701,1712,2152,1806,
>  1821,1983,2107,1678,1065,1911,2264,1615,1795)( 680,2069,1523,1126,
>  1735,1819,2216,2212,2251,1915,1925,1928,1810,1640,1107)
> ( 690,2180, 736,1608,1896,2165, 988,1433,1434,1826,2009,1590,2110,1992,
>  2221)( 691,1908,1758,1299,1779,1837,1420, 714, 715, 895,1090, 692,
>   952,1101, 755)( 697,1221,1723, 735,1108,2193,1348,1927,1904,1742,
>  1493,1587,1793,2035,2044)( 698,1428,1062, 813, 798, 790,1485,1265,
>   928, 708,1906,1449,1224, 932, 887)( 700,1397,1701,1016,1564,2060,
>  1722,1893,2209,2039,2276,1962,1563,1360,1609)( 722,1583, 959, 962,
>  1168,1087,1007, 828,1769,1289, 905,1601,1220,1448,1456)
> ( 748, 749,1453,1412,2182,1442,1481,1873,1932,2096,1374,2029,2263,2293,
>  1862)( 750, 751,1861,1635,1617,2042,1368,1788,1094,1759,1260,1835,
>  1632,2278,2192)( 764,1558, 818, 819,1557,1446,1530,1739,1705,1159,
>  1546,1717, 816,1730,1662)( 782,1839,1447,1774,1311, 876,1103,1036,
>  1029, 808,1372,1120, 999,1048,1175)( 794,1219,1071,1660,1661,2087,
>  1663,2284,1665,1651,1246,1146,1568,1569,1642)( 826,1369,1123)
> ( 834,2145,1951,1125,1636,1462,1940,1972, 934,1725,2101,2105,2200,2037,
>  954)( 865,1777, 869,1295,1671)( 916,1596,1650,2255,2238,1358,1604,
>  1997,1040,2244,1868,2259,2032,1864,2143)( 944,2125,1341,1092,1909,
>  2080,2227,2111,1515,2108,1228,1562,1618,2157,2036)( 956,1402,2133,
>  2265,2094,1714,2135,1521,2052,2134,1579,1580,1920,1405,1849)
> ( 965,1761,1400)( 970, 971,1133,1001,1857,2272,2132, 981,2269,2287,
>  1727,1917,1919,2256, 987)( 975,1855,1470,1565,2149,1853,2115,1968,
>  1225,1801,1859,1002,1478,1443,1044)( 976,1176,2249,1501,1033,1625,
>  1875,1414,1882,2118,1784,1763,1852,1479,1480)( 991,2065,1623,2122,
>  1581,1817,1589,2198,2282,1603,1913,1967,1969,2215,1724)
> ( 993,1923,2297,2159,2225,2226,2217,1517,2294,2171,2210,2211,2295,2181,
>  1042)(1009,2148,1752,2161,1921,1867,1938,1816,1993,1803,1359,1227,
>  1525,1903,1043)(1020,1902,2273,1606,1638,1791,2034,1886,2002,2155,
>  2025,2075,2023,2150,1933)(1031,1957,1934,1892,1836,1841,1404,1851,
>  2128,1256,1616,2205,2059,1881,2147)(1032,1215,1799,2021,2239,1422,
>  1719,1720,1956,2224,1041,1874,1418,1483,2231)(1034,1677,2103,1939,
>  1946,1884,1918,1445,2051,1631,2070,2197,2008,2257,1922)
> (1072,1782,2187,2274,2286,2260,2137,1691,1785,1856,1387,1773,1847,2006,
>  1287)(1082,1592,2104,1571,1498,1124,2207,1385,1389,1396,1800,1965,
>  1129,1254,1766)(1089,1963,1693,2130,1935,1458,1813,2233,2007,1953,
>  1825,2254,1966,1854,2191)(1105,1970,1507,1955,2169,1384,1303,1437,
>  2268,2299,2079,1949,2091,1425,1971)(1134,1959,1321,2012,1269,1999,
>  1818,2136,1492,1905,1659,2247,1435,2058,2072)(1189,2236,2084,2288,
>  1482,1500,1503,1559,2141,1593,2201,1879,2195,2250,1504)
> (1245,2113,1914,2246,2144,1375,1828,1979,1474,1871,1716,1343,2013,2186,
>  2112)(1313,1754,1755,1532,1732,2146,2076,1728,1974,2099,2020,2077,
>  2049,1584,1748)(1322,1958,2028,2243,2208,1894,1980,2245,2196,1924,
>  2102,2019,1490,1328,1829)(1344,1398,1415,1610,2291,1362,1551,2235,
>  2114,1353,1556,2158,2047,1823,1843)(1388,2204,2063,1756,1797,1461,
>  1929,1597,2151,1600,2026,2170,1952,1576,2162)(1409,1670,2296,2277,
>  1738,2219,2167,2160,2095,1981,1822,2184,2242,2055,1872)
> (1410,1977,1950,2179,1878,2194,1863,2176,1765,2129,1883,1945,2234,1519,
>  1522)(1411,2056,1877,2203,2066,1770,2228,1688,2127,1942,1984,1524,
>  2290,1858,1890)(1424,1804,2123,1762,1848,2232,1994,2166,2248,1499,
>  1954,1513,2038,2199,1866)(1466,1960,1690,1937,1910,1814,1494,2022,
>  1995,1749,1622,1869,2168,1865,2015)(1467,1505,2048,2279,2267,2175,
>  1757,2041,2131,2223,1987,1669,1944,1947,1591)(1468,1594,1811,1473,
>  1936,2281,2213,1887,2140,2178,2202,2173,1627,1830,1767)
> (1516,1802,1870,2014,1982,2005,2050,2073,1721,2100,2188,2174,1539,1746,
>  1736)(1620,1809,2062,2285,2085,1943,1975,1964,1897,1898,2220,1888,
>  1889,1991,1808) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Co(2)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 42305421312000, 1 ]

# $Co_3$ on 276 points
gap> g:= Group(
> (4,6)(5,10)(7,13)(8,16)(9,11)(12,21)(14,24)(15,27)
> (17,29)(20,34)(22,37)(23,40)(25,46)(26,47)(28,44)(31,53)
> (33,50)(35,57)(36,59)(38,63)(41,66)(42,45)(43,72)(48,81)
> (49,83)(52,89)(54,92)(55,56)(58,99)(60,62)(61,73)(64,109)
> (67,112)(68,75)(69,116)(70,78)(71,120)(74,123)(77,102)(82,91)
> (84,136)(85,135)(86,138)(87,141)(90,145)(93,151)(94,153)(95,147)
> (96,155)(97,149)(98,150)(101,159)(103,127)(104,163)(105,131)(106,165)
> (107,167)(110,170)(114,175)(115,130)(117,179)(118,178)(119,129)(121,183)
> (124,160)(125,182)(128,161)(133,188)(134,193)(137,196)(139,202)(140,204)
> (142,190)(143,208)(146,209)(148,194)(152,216)(154,219)(156,222)(157,215)
> (158,205)(162,224)(164,185)(166,226)(171,228)(173,232)(176,177)(180,195)
> (181,241)(184,242)(187,244)(191,245)(192,211)(197,250)(198,217)(200,252)
> (201,253)(203,256)(206,257)(207,237)(212,249)(213,238)(214,259)(218,240)
> (220,263)(221,261)(223,262)(225,235)(229,265)(230,266)(233,243)(236,239)
> (246,270)(247,272)(248,271)(251,260)(254,255)(258,269)(268,276)(273,274),
> 
> (4,8)(6,12)(7,14)(9,17)(10,19)(11,20)(13,22)(15,27)
> (16,21)(18,31)(23,41)(24,37)(26,32)(28,33)(29,34)(35,54)
> (36,50)(39,48)(40,67)(42,69)(43,61)(44,59)(45,77)(46,80)
> (49,84)(51,87)(55,94)(56,96)(57,98)(58,93)(60,101)(62,105)
> (63,108)(65,110)(66,112)(68,114)(70,118)(71,76)(72,123)(73,74)
> (75,104)(78,128)(79,130)(82,117)(83,134)(85,137)(86,139)(88,142)
> (89,144)(91,148)(92,150)(95,154)(97,156)(99,157)(102,116)(103,127)
> (106,107)(109,169)(111,171)(119,181)(121,126)(122,145)(124,162)(125,132)
> (129,187)(131,159)(135,195)(136,193)(138,200)(143,206)(146,211)(147,212)
> (149,214)(151,215)(152,176)(153,155)(160,225)(161,178)(163,175)(164,192)
> (165,226)(166,167)(168,205)(172,204)(177,238)(179,194)(180,196)(184,189)
> (185,209)(186,232)(188,234)(198,223)(199,243)(202,252)(203,220)(207,258)
> (208,254)(210,250)(213,216)(217,236)(218,221)(219,249)(222,259)(224,235)
> (230,246)(231,253)(237,247)(239,262)(240,248)(241,244)(245,267)(251,266)
> (255,257)(256,273)(260,270)(261,271)(263,274)(265,275)(268,276)(269,272),
> 
> (2,4)(3,6)(5,10)(9,13)(12,19)(14,25)(16,27)(17,30)
> (20,35)(21,32)(22,38)(23,42)(24,45)(28,49)(29,51)(31,54)
> (33,55)(34,56)(36,60)(37,62)(39,65)(40,46)(41,68)(43,71)
> (44,75)(48,82)(50,57)(52,64)(53,91)(58,100)(59,63)(61,103)
> (66,83)(67,113)(69,117)(70,119)(73,124)(74,106)(76,105)(77,127)
> (78,129)(79,131)(80,133)(81,92)(85,86)(87,101)(89,135)(90,146)
> (95,97)(96,98)(99,111)(102,160)(104,107)(108,162)(109,138)(110,114)
> (112,172)(115,176)(116,177)(118,180)(123,185)(125,164)(128,186)(130,179)
> (132,188)(134,194)(137,198)(139,203)(140,158)(141,205)(142,207)(144,161)
> (145,209)(148,211)(151,208)(153,216)(154,220)(156,223)(157,196)(159,204)
> (165,182)(168,224)(169,199)(170,175)(171,221)(173,230)(174,235)(178,195)
> (181,218)(183,242)(189,227)(190,240)(191,247)(192,238)(193,213)(197,215)
> (201,254)(202,255)(206,258)(212,236)(214,229)(217,250)(219,262)(222,263)
> (225,234)(228,259)(231,268)(233,244)(237,241)(239,269)(245,271)(246,248)
> (249,257)(252,260)(253,256)(261,265)(264,274)(267,276)(270,272)(273,275),
> 
> (1,2)(4,9)(6,11)(7,13)(8,17)(12,20)(14,22)(15,27)
> (16,29)(21,34)(23,41)(24,37)(26,48)(28,36)(32,39)(33,50)
> (35,58)(38,64)(40,66)(42,70)(43,74)(44,59)(45,78)(47,81)
> (49,85)(51,88)(54,93)(55,56)(57,99)(60,68)(61,73)(62,75)
> (63,109)(65,111)(67,112)(69,118)(71,121)(72,123)(76,126)(77,128)
> (82,95)(83,135)(84,137)(86,119)(87,142)(91,147)(92,151)(94,96)
> (97,143)(98,157)(101,114)(102,161)(103,127)(104,105)(106,166)(107,167)
> (108,169)(110,171)(113,174)(116,178)(117,154)(120,183)(124,162)(125,184)
> (129,138)(131,163)(132,189)(133,191)(134,195)(136,196)(139,181)(140,201)
> (141,190)(148,212)(149,208)(150,215)(152,217)(153,155)(156,206)(159,175)
> (160,224)(165,226)(170,228)(172,231)(173,233)(176,236)(177,239)(179,219)
> (180,193)(182,242)(186,199)(187,200)(188,245)(194,249)(198,216)(202,241)
> (203,207)(204,253)(213,223)(214,254)(218,221)(220,258)(222,257)(225,235)
> (227,264)(230,260)(232,243)(234,267)(237,256)(238,262)(240,261)(244,252)
> (246,270)(247,273)(248,271)(251,266)(255,259)(263,269)(268,276)(272,274)
> );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Co(3)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 495766656000, 1 ]

# cube
gap> g := Group(
>   (1,3,8,6)(2,5,7,4)(9,48,15,12)(10,47,16,13)(11,46,17,14),
>   (9,11,26,24)(10,19,25,18)(1,12,33,41)(4,20,36,44)(6,27,38,46),
>   (12,14,29,27)(13,21,28,20)(6,15,35,26)(7,22,34,19)(8,30,33,11),
>   (15,17,32,30)(16,23,31,22)(3,43,35,14)(5,45,37,21)(8,48,40,29),
>   (33,35,40,38)(34,37,39,36)(24,27,30,43)(25,28,31,42)(26,29,32,41),
>   (41,43,48,46)(42,45,47,44)(1,24,40,17)(2,18,39,23)(3,9,38,32) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Z(2)
Group
 | A(8) ~ A(3,2) = L(4,2) ~ D(3,2) = O+(6,2)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | A(12)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 43252003274489856000, 21626001637244928000, 1072718335180800, 490497638400, 
  2048, 2, 1 ]

# gl10.2
gap> g:=
> Group( (257,513)(258,514)(259,515)(260,516)(261,517)(262,518)(263,519)
> (264,520)(265,521)(266,522)(267,523)(268,524)(269,525)(270,526)
> (271,527)(272,528)(273,529)(274,530)(275,531)(276,532)(277,533)
> (278,534)(279,535)(280,536)(281,537)(282,538)(283,539)(284,540)
> (285,541)(286,542)(287,543)(288,544)(289,545)(290,546)(291,547)
> (292,548)(293,549)(294,550)(295,551)(296,552)(297,553)(298,554)
> (299,555)(300,556)(301,557)(302,558)(303,559)(304,560)(305,561)
> (306,562)(307,563)(308,564)(309,565)(310,566)(311,567)(312,568)
> (313,569)(314,570)(315,571)(316,572)(317,573)(318,574)(319,575)
> (320,576)(321,577)(322,578)(323,579)(324,580)(325,581)(326,582)
> (327,583)(328,584)(329,585)(330,586)(331,587)(332,588)(333,589)
> (334,590)(335,591)(336,592)(337,593)(338,594)(339,595)(340,596)
> (341,597)(342,598)(343,599)(344,600)(345,601)(346,602)(347,603)
> (348,604)(349,605)(350,606)(351,607)(352,608)(353,609)(354,610)
> (355,611)(356,612)(357,613)(358,614)(359,615)(360,616)(361,617)
> (362,618)(363,619)(364,620)(365,621)(366,622)(367,623)(368,624)
> (369,625)(370,626)(371,627)(372,628)(373,629)(374,630)(375,631)
> (376,632)(377,633)(378,634)(379,635)(380,636)(381,637)(382,638)
> (383,639)(384,640)(385,641)(386,642)(387,643)(388,644)(389,645)
> (390,646)(391,647)(392,648)(393,649)(394,650)(395,651)(396,652)
> (397,653)(398,654)(399,655)(400,656)(401,657)(402,658)(403,659)
> (404,660)(405,661)(406,662)(407,663)(408,664)(409,665)(410,666)
> (411,667)(412,668)(413,669)(414,670)(415,671)(416,672)(417,673)
> (418,674)(419,675)(420,676)(421,677)(422,678)(423,679)(424,680)
> (425,681)(426,682)(427,683)(428,684)(429,685)(430,686)(431,687)
> (432,688)(433,689)(434,690)(435,691)(436,692)(437,693)(438,694)
> (439,695)(440,696)(441,697)(442,698)(443,699)(444,700)(445,701)
> (446,702)(447,703)(448,704)(449,705)(450,706)(451,707)(452,708)
> (453,709)(454,710)(455,711)(456,712)(457,713)(458,714)(459,715)
> (460,716)(461,717)(462,718)(463,719)(464,720)(465,721)(466,722)
> (467,723)(468,724)(469,725)(470,726)(471,727)(472,728)(473,729)
> (474,730)(475,731)(476,732)(477,733)(478,734)(479,735)(480,736)
> (481,737)(482,738)(483,739)(484,740)(485,741)(486,742)(487,743)
> (488,744)(489,745)(490,746)(491,747)(492,748)(493,749)(494,750)
> (495,751)(496,752)(497,753)(498,754)(499,755)(500,756)(501,757)
> (502,758)(503,759)(504,760)(505,761)(506,762)(507,763)(508,764)
> (509,765)(510,766)(511,767)(512,768), (   2,   3,   5,   9,  17,  33,
>    65, 129, 257, 513)(   4,   7,  13,  25,  49,  97, 193, 385, 769, 514
>  )(   6,  11,  21,  41,  81, 161, 321, 641, 258, 515)(   8,  15,  29,
>    57, 113, 225, 449, 897, 770, 516)(  10,  19,  37,  73, 145, 289,
>   577, 130, 259, 517)(  12,  23,  45,  89, 177, 353, 705, 386, 771, 518
>  )(  14,  27,  53, 105, 209, 417, 833, 642, 260, 519)(  16,  31,  61,
>   121, 241, 481, 961, 898, 772, 520)(  18,  35,  69, 137, 273, 545,
>    66, 131, 261, 521)(  20,  39,  77, 153, 305, 609, 194, 387, 773, 522
>  )(  22,  43,  85, 169, 337, 673, 322, 643, 262, 523)(  24,  47,  93,
>   185, 369, 737, 450, 899, 774, 524)(  26,  51, 101, 201, 401, 801,
>   578, 132, 263, 525)(  28,  55, 109, 217, 433, 865, 706, 388, 775, 526
>  )(  30,  59, 117, 233, 465, 929, 834, 644, 264, 527)(  32,  63, 125,
>   249, 497, 993, 962, 900, 776, 528)(  34,  67, 133, 265, 529)
> (  36,  71, 141, 281, 561,  98, 195, 389, 777, 530)(  38,  75, 149,
>   297, 593, 162, 323, 645, 266, 531)(  40,  79, 157, 313, 625, 226,
>   451, 901, 778, 532)(  42,  83, 165, 329, 657, 290, 579, 134, 267, 533
>  )(  44,  87, 173, 345, 689, 354, 707, 390, 779, 534)(  46,  91, 181,
>   361, 721, 418, 835, 646, 268, 535)(  48,  95, 189, 377, 753, 482,
>   963, 902, 780, 536)(  50,  99, 197, 393, 785, 546,  68, 135, 269, 537
>  )(  52, 103, 205, 409, 817, 610, 196, 391, 781, 538)(  54, 107, 213,
>   425, 849, 674, 324, 647, 270, 539)(  56, 111, 221, 441, 881, 738,
>   452, 903, 782, 540)(  58, 115, 229, 457, 913, 802, 580, 136, 271, 541
>  )(  60, 119, 237, 473, 945, 866, 708, 392, 783, 542)(  62, 123, 245,
>   489, 977, 930, 836, 648, 272, 543)(  64, 127, 253, 505,1009, 994,
>   964, 904, 784, 544)(  70, 139, 277, 553,  82, 163, 325, 649, 274, 547
>  )(  72, 143, 285, 569, 114, 227, 453, 905, 786, 548)(  74, 147, 293,
>   585, 146, 291, 581, 138, 275, 549)(  76, 151, 301, 601, 178, 355,
>   709, 394, 787, 550)(  78, 155, 309, 617, 210, 419, 837, 650, 276, 551
>  )(  80, 159, 317, 633, 242, 483, 965, 906, 788, 552)(  84, 167, 333,
>   665, 306, 611, 198, 395, 789, 554)(  86, 171, 341, 681, 338, 675,
>   326, 651, 278, 555)(  88, 175, 349, 697, 370, 739, 454, 907, 790, 556
>  )(  90, 179, 357, 713, 402, 803, 582, 140, 279, 557)(  92, 183, 365,
>   729, 434, 867, 710, 396, 791, 558)(  94, 187, 373, 745, 466, 931,
>   838, 652, 280, 559)(  96, 191, 381, 761, 498, 995, 966, 908, 792, 560
>  )( 100, 199, 397, 793, 562)( 102, 203, 405, 809, 594, 164, 327, 653,
>   282, 563)( 104, 207, 413, 825, 626, 228, 455, 909, 794, 564)
> ( 106, 211, 421, 841, 658, 292, 583, 142, 283, 565)( 108, 215, 429,
>   857, 690, 356, 711, 398, 795, 566)( 110, 219, 437, 873, 722, 420,
>   839, 654, 284, 567)( 112, 223, 445, 889, 754, 484, 967, 910, 796, 568
>  )( 116, 231, 461, 921, 818, 612, 200, 399, 797, 570)( 118, 235, 469,
>   937, 850, 676, 328, 655, 286, 571)( 120, 239, 477, 953, 882, 740,
>   456, 911, 798, 572)( 122, 243, 485, 969, 914, 804, 584, 144, 287, 573
>  )( 124, 247, 493, 985, 946, 868, 712, 400, 799, 574)( 126, 251, 501,
>  1001, 978, 932, 840, 656, 288, 575)( 128, 255, 509,1017,1010, 996,
>   968, 912, 800, 576)( 148, 295, 589, 154, 307, 613, 202, 403, 805, 586
>  )( 150, 299, 597, 170, 339, 677, 330, 659, 294, 587)( 152, 303, 605,
>   186, 371, 741, 458, 915, 806, 588)( 156, 311, 621, 218, 435, 869,
>   714, 404, 807, 590)( 158, 315, 629, 234, 467, 933, 842, 660, 296, 591
>  )( 160, 319, 637, 250, 499, 997, 970, 916, 808, 592)( 166, 331, 661,
>   298, 595)( 168, 335, 669, 314, 627, 230, 459, 917, 810, 596)
> ( 172, 343, 685, 346, 691, 358, 715, 406, 811, 598)( 174, 347, 693,
>   362, 723, 422, 843, 662, 300, 599)( 176, 351, 701, 378, 755, 486,
>   971, 918, 812, 600)( 180, 359, 717, 410, 819, 614, 204, 407, 813, 602
>  )( 182, 363, 725, 426, 851, 678, 332, 663, 302, 603)( 184, 367, 733,
>   442, 883, 742, 460, 919, 814, 604)( 188, 375, 749, 474, 947, 870,
>   716, 408, 815, 606)( 190, 379, 757, 490, 979, 934, 844, 664, 304, 607
>  )( 192, 383, 765, 506,1011, 998, 972, 920, 816, 608)( 206, 411, 821,
>   618, 212, 423, 845, 666, 308, 615)( 208, 415, 829, 634, 244, 487,
>   973, 922, 820, 616)( 214, 427, 853, 682, 340, 679, 334, 667, 310, 619
>  )( 216, 431, 861, 698, 372, 743, 462, 923, 822, 620)( 220, 439, 877,
>   730, 436, 871, 718, 412, 823, 622)( 222, 443, 885, 746, 468, 935,
>   846, 668, 312, 623)( 224, 447, 893, 762, 500, 999, 974, 924, 824, 624
>  )( 232, 463, 925, 826, 628)( 236, 471, 941, 858, 692, 360, 719, 414,
>   827, 630)( 238, 475, 949, 874, 724, 424, 847, 670, 316, 631)
> ( 240, 479, 957, 890, 756, 488, 975, 926, 828, 632)( 246, 491, 981,
>   938, 852, 680, 336, 671, 318, 635)( 248, 495, 989, 954, 884, 744,
>   464, 927, 830, 636)( 252, 503,1005, 986, 948, 872, 720, 416, 831, 638
>  )( 254, 507,1013,1002, 980, 936, 848, 672, 320, 639)( 256, 511,1021,
>  1018,1012,1000, 976, 928, 832, 640)( 342, 683)( 344, 687, 350, 699,
>   374, 747, 470, 939, 854, 684)( 348, 695, 366, 731, 438, 875, 726,
>   428, 855, 686)( 352, 703, 382, 763, 502,1003, 982, 940, 856, 688)
> ( 364, 727, 430, 859, 694)( 368, 735, 446, 891, 758, 492, 983, 942,
>   860, 696)( 376, 751, 478, 955, 886, 748, 472, 943, 862, 700)
> ( 380, 759, 494, 987, 950, 876, 728, 432, 863, 702)( 384, 767, 510,
>  1019,1014,1004, 984, 944, 864, 704)( 440, 879, 734, 444, 887, 750,
>   476, 951, 878, 732)( 448, 895, 766, 508,1015,1006, 988, 952, 880, 736
>  )( 480, 959, 894, 764, 504,1007, 990, 956, 888, 752)( 496, 991, 958,
>   892, 760)( 512,1023,1022,1020,1016,1008, 992, 960, 896, 768), 
> ( 257, 769)( 258, 770)( 259, 771)( 260, 772)( 261, 773)( 262, 774)
> ( 263, 775)( 264, 776)( 265, 777)( 266, 778)( 267, 779)( 268, 780)
> ( 269, 781)( 270, 782)( 271, 783)( 272, 784)( 273, 785)( 274, 786)
> ( 275, 787)( 276, 788)( 277, 789)( 278, 790)( 279, 791)( 280, 792)
> ( 281, 793)( 282, 794)( 283, 795)( 284, 796)( 285, 797)( 286, 798)
> ( 287, 799)( 288, 800)( 289, 801)( 290, 802)( 291, 803)( 292, 804)
> ( 293, 805)( 294, 806)( 295, 807)( 296, 808)( 297, 809)( 298, 810)
> ( 299, 811)( 300, 812)( 301, 813)( 302, 814)( 303, 815)( 304, 816)
> ( 305, 817)( 306, 818)( 307, 819)( 308, 820)( 309, 821)( 310, 822)
> ( 311, 823)( 312, 824)( 313, 825)( 314, 826)( 315, 827)( 316, 828)
> ( 317, 829)( 318, 830)( 319, 831)( 320, 832)( 321, 833)( 322, 834)
> ( 323, 835)( 324, 836)( 325, 837)( 326, 838)( 327, 839)( 328, 840)
> ( 329, 841)( 330, 842)( 331, 843)( 332, 844)( 333, 845)( 334, 846)
> ( 335, 847)( 336, 848)( 337, 849)( 338, 850)( 339, 851)( 340, 852)
> ( 341, 853)( 342, 854)( 343, 855)( 344, 856)( 345, 857)( 346, 858)
> ( 347, 859)( 348, 860)( 349, 861)( 350, 862)( 351, 863)( 352, 864)
> ( 353, 865)( 354, 866)( 355, 867)( 356, 868)( 357, 869)( 358, 870)
> ( 359, 871)( 360, 872)( 361, 873)( 362, 874)( 363, 875)( 364, 876)
> ( 365, 877)( 366, 878)( 367, 879)( 368, 880)( 369, 881)( 370, 882)
> ( 371, 883)( 372, 884)( 373, 885)( 374, 886)( 375, 887)( 376, 888)
> ( 377, 889)( 378, 890)( 379, 891)( 380, 892)( 381, 893)( 382, 894)
> ( 383, 895)( 384, 896)( 385, 897)( 386, 898)( 387, 899)( 388, 900)
> ( 389, 901)( 390, 902)( 391, 903)( 392, 904)( 393, 905)( 394, 906)
> ( 395, 907)( 396, 908)( 397, 909)( 398, 910)( 399, 911)( 400, 912)
> ( 401, 913)( 402, 914)( 403, 915)( 404, 916)( 405, 917)( 406, 918)
> ( 407, 919)( 408, 920)( 409, 921)( 410, 922)( 411, 923)( 412, 924)
> ( 413, 925)( 414, 926)( 415, 927)( 416, 928)( 417, 929)( 418, 930)
> ( 419, 931)( 420, 932)( 421, 933)( 422, 934)( 423, 935)( 424, 936)
> ( 425, 937)( 426, 938)( 427, 939)( 428, 940)( 429, 941)( 430, 942)
> ( 431, 943)( 432, 944)( 433, 945)( 434, 946)( 435, 947)( 436, 948)
> ( 437, 949)( 438, 950)( 439, 951)( 440, 952)( 441, 953)( 442, 954)
> ( 443, 955)( 444, 956)( 445, 957)( 446, 958)( 447, 959)( 448, 960)
> ( 449, 961)( 450, 962)( 451, 963)( 452, 964)( 453, 965)( 454, 966)
> ( 455, 967)( 456, 968)( 457, 969)( 458, 970)( 459, 971)( 460, 972)
> ( 461, 973)( 462, 974)( 463, 975)( 464, 976)( 465, 977)( 466, 978)
> ( 467, 979)( 468, 980)( 469, 981)( 470, 982)( 471, 983)( 472, 984)
> ( 473, 985)( 474, 986)( 475, 987)( 476, 988)( 477, 989)( 478, 990)
> ( 479, 991)( 480, 992)( 481, 993)( 482, 994)( 483, 995)( 484, 996)
> ( 485, 997)( 486, 998)( 487, 999)( 488,1000)( 489,1001)( 490,1002)
> ( 491,1003)( 492,1004)( 493,1005)( 494,1006)( 495,1007)( 496,1008)
> ( 497,1009)( 498,1010)( 499,1011)( 500,1012)( 501,1013)( 502,1014)
> ( 503,1015)( 504,1016)( 505,1017)( 506,1018)( 507,1019)( 508,1020)
> ( 509,1021)( 510,1022)( 511,1023)( 512,1024) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | A(9,2) = L(10,2) 
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 366440137299948128422802227200, 1 ]

# $J_2$ on 100 points
gap> g:= Group( (2,3,4,5,6,7,8)(9,10,11,12,13,14,15)
> (16,17,18,19,20,21,22)(23,24,25,26,27,28,29)(30,31,32,33,34,35,36)
> (37,38,39,40,41,42,43)(44,45,46,47,48,49,50)(51,52,53,54,55,56,57)
> (58,59,60,61,62,63,64)(65,66,67,68,69,70,71)(72,73,74,75,76,77,78)
> (79,80,81,82,83,84,85)(86,87,88,89,90,91,92)(93,94,95,96,97,98,99),
> (1,2,9,16,23,20,30,17)(3,35,13,29,31,24,25,11)(4,26,27,7)(5,21,14,10)
> (6,19,32,36)(8,18,28,22,15,12,33,34)(38,92,67,77,99,89,49,84)
> (39,59,82,46,88,54,52,68)(40,55,47,81,75,95,61,78)
> (41,44,63,58,72,65,50,51)(42,76,53,93,86,80,79,57)
> (43,85,48,70,96,83,66,94)(45,97)(56,87)(60,71,91,69,90,73,64,74)
> (62,98),
> (1,100)(2,74)(3,73)(4,72)(5,78)(6,77)(7,76)(8,75)(9,34)(10,33)(11,32)
> (12,31)(13,30)(14,36)(15,35)(16,71)(17,70)(18,69)(19,68)(20,67)(21,66)
> (22,65)(23,53)(24,52)(25,51)(26,57)(27,56)(28,55)(29,54)(37,91)(38,90)
> (39,89)(40,88)(41,87)(42,86)(43,92)(44,99)(45,98)(46,97)(47,96)(48,95)
> (49,94)(50,93)(58,85)(59,84)(60,83)(61,82)(62,81)(63,80)(64,79) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | HJ = J(2) = F(5-)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 604800, 1 ]

# neum on 240 points
gap> g:=
> Group( (  3,  8,  6)(  4, 16, 23)(  5, 86,119)(  7, 91,149)
> (  9, 89, 14)( 10,164, 18)( 11, 19, 20)( 12, 74,120)( 13,101, 28)
> ( 15, 58, 30)( 17, 45, 35)( 21, 36, 22)( 24, 67, 25)( 26,133, 57)
> ( 27,135, 80)( 29,165,136)( 31,177, 32)( 33, 93, 34)( 37, 79, 49)
> ( 38, 66, 63)( 39, 92, 55)( 40,114,134)( 41, 68,115)( 42, 51, 43)
> ( 44, 84, 46)( 47, 78,116)( 48,159, 70)( 50,175, 75)( 52,211, 53)
> ( 54,212,188)( 59,141,142)( 60,129,110)( 61,231,230)( 62,140,139)
> ( 64, 72,107)( 65,184,172)( 69,143, 83)( 71,128,195)( 73,122,192)
> ( 76,225,228)( 77, 88,170)( 81, 87,137)( 82,227,154)( 85,109,108)
> ( 90,173,193)( 94,160,132)( 95, 99,118)( 96,213,148)( 97,218,150)
> ( 98,111,127)(100,124,117)(102,229,190)(103,167,138)(104,185,147)
> (105,180,174)(106,125,153)(112,113,186)(121,131,126)(123,168,205)
> (130,196,233)(144,197,223)(145,146,166)(151,155,152)(156,215,217)
> (157,207,187)(158,178,208)(161,226,232)(162,182,171)(163,181,198)
> (169,201,176)(179,238,210)(183,191,206)(189,209,236)(194,203,220)
> (200,222,221)(202,219,204)(214,224,234)(216,235,240), (  1,  3,  2)
> (  4,146,151)(  5, 11, 41)(  7, 66,109)(  9, 27, 28)( 10,137,136)
> ( 12, 40, 15)( 13, 86, 32)( 14, 85,153)( 16, 26, 17)( 18,129,133)
> ( 19,135,114)( 20,108, 73)( 21, 99, 56)( 22, 94, 95)( 23,140, 77)
> ( 24,150, 54)( 25,102, 96)( 29, 35, 78)( 30,100,122)( 31, 37,192)
> ( 33,190,213)( 34, 97,105)( 36,160,118)( 38, 68, 74)( 39, 60, 65)
> ( 42,184, 75)( 43, 62, 59)( 44,115,117)( 45, 92,141)( 46, 80, 79)
> ( 47, 69, 88)( 48, 67,212)( 49,106,120)( 50, 71,155)( 51,166,165)
> ( 52,148,159)( 53,173,180)( 55, 81,152)( 57,195,113)( 58, 89, 72)
> ( 63, 64,177)( 70, 93,174)( 76, 98,182)( 82,161,147)( 83,110,145)
> ( 84,107,131)( 87,112,139)( 90,218,229)( 91,134,126)(101,124,149)
> (103,104,206)(111,181,228)(116,186,172)(119,121,125)(123,194,157)
> (127,223,225)(128,143,142)(130,220,222)(138,154,226)(144,198,171)
> (156,234,187)(158,237,236)(162,163,197)(164,170,175)(167,183,185)
> (168,221,240)(169,216,217)(176,224,202)(178,189,179)(188,211,193)
> (191,227,232)(196,207,215)(199,239,231)(200,201,233)(203,204,214)
> (205,219,235)(208,209,210), (  2, 11, 16)(  3, 17, 15)(  4, 47, 10)
> (  5, 12,  9)(  6, 39, 43)(  7,162,147)(  8, 34, 25)( 13,166,184)
> ( 14, 86,118)( 18,126, 19)( 20, 21, 24)( 22, 23, 93)( 26, 28, 27)
> ( 29,185,182)( 30, 48, 31)( 32,128, 33)( 35, 36, 42)( 38,187,109)
> ( 40, 61, 41)( 44, 73,201)( 45, 53, 78)( 46,112,227)( 49,219,133)
> ( 50, 67, 71)( 51,131, 52)( 54,174, 83)( 55, 56, 58)( 57,139,220)
> ( 59,170, 60)( 62,231, 63)( 64,199, 65)( 66,189,114)( 68,135,194)
> ( 69,156,106)( 70,116,121)( 72,204,209)( 74,111,120)( 75,159, 92)
> ( 76,190,154)( 77,210,110)( 79, 80,222)( 81,208,158)( 82,235,228)
> ( 84,167,180)( 85,101,107)( 87,232,238)( 88,129,178)( 89, 94,119)
> ( 90,229,144)( 91,205,197)( 95, 99,117)( 96,169, 97)( 98,124,160)
> (100,127,132)(102,215,103)(104,196,105)(108,145,203)(113,130,191)
> (115,237,140)(122,225,155)(123,136,181)(125,233,214)(134,146,157)
> (137,179,161)(138,148,149)(141,226,142)(143,153,173)(150,152,186)
> (151,163,234)(164,175,177)(165,213,183)(168,218,176)(171,188,224)
> (172,236,200)(192,212,223)(193,198,240)(202,221,230)(206,217,216) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | A(2,4) = L(3,4)
Group
 | Z(2)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 40320, 2, 1 ]

# regular
gap> g:= PrimitiveGroup( 11, 6 );;
gap> elms:= AsList( g );;
gap> gens:= Concatenation( List( GeneratorsOfGroup( g ),
>            x -> [ PermList( List( [ 1 .. 7920 ],
>                       i -> Position( elms, elms[i] * x ) ) ),
>                   PermList( List( [ 1 .. 7920 ],
>                       i -> Position( elms, x^-1 * elms[i] ) ) ) ] ) );;
gap> reg:= Group( gens );;
gap> CustomDisplayCompositionSeries( g );
Group
 | M(11)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 7920, 1 ]
gap> # $S_5 \wr S_5$ on 3125 points. 
gap> l:= [ (1,2,3,4,5), (1,2), (1,6,11,16,21)(2,7,12,17,22)(3,8,13,18,23)
>          (4,9,14,19,24)(5,10,15,20,25), (1,6)(2,7)(3,8)(4,9)(5,10) ];;
gap> tuptonum:= tup -> tup * [ 1, 5, 25, 125, 625 ] - 15430;;
gap> numtotup:= function( num )
>    local tup,i;
>    tup:= [];
>    num:= num-1; 
>    for i in [ 1 .. 5 ] do
>      tup[i]:= (num mod 5) + 1 + 5*(i-1);
>      num:= (num - tup[i] + 5*(i-1) + 1)/5;
>    od;
>    return tup;
>    end;;
gap> gens:= [];;
gap> for j in [ 1 .. 4 ] do
>      gens[j]:= [];
>      for i in [ 1 .. 3125 ] do
>        tup:= numtotup(i);
>        for k in [ 1 .. 5 ] do 
>          tup[k]:= tup[k]^l[j];
>        od;
>        Sort(tup);
>        gens[j][i]:=tuptonum(tup);
>      od;
>    od;
gap> g:= Group( List( gens, PermList ), () );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Z(2)
Group
 | Z(2)
Group
 | A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U(2,\
4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)
Group
 | Z(2)
Group
 | A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U(2,\
4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)
Group
 | Z(2)
Group
 | A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U(2,\
4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)
Group
 | Z(2)
Group
 | A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U(2,\
4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)
Group
 | Z(2)
Group
 | A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U(2,\
4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)
Group
 | A(5) ~ A(1,4) = L(2,4) ~ B(1,4) = O(3,4) ~ C(1,4) = S(2,4) ~ 2A(1,4) = U(2,\
4) ~ A(1,5) = L(2,5) ~ B(1,5) = O(3,5) ~ C(1,5) = S(2,5) ~ 2A(1,5) = U(2,5)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 2985984000000, 1492992000000, 746496000000, 12441600000, 777600000, 1 ]

# sol768.gen
gap> g:=
> Group( (  1,  4)(  2,  5)(  3, 73)(  9,175, 28,188, 12,172)
> ( 10,177,132,221, 13,174)( 11,176, 75,552, 14,173)( 15,166)( 16,168)
> ( 17,167)( 18,482)( 19,217)( 20,612)( 21,394, 24,530, 42,164)
> ( 22,395, 25,209,141,165)( 23,163, 26,614, 86,388)( 29,436, 43,512, 33,
>  186)( 30,619, 47,498, 34,196)( 31,181,424,201,454,184)
> ( 32,437,445,622, 35,180)( 36,462,375,185,461,474)( 37,169)
> ( 38,178, 39,455,475,182)( 40,489, 41,434,444,191)( 44,528, 51,187,440,
>  62)( 45,446,467,415, 57,531)( 46,194,376,527,515, 65)( 48,476, 55,504,
>  404,481)( 49, 66, 50, 64, 54, 71)( 52,532,441,192,611, 69)
> ( 53, 70,373,193,208, 63)( 56,183, 58,179,435,190)( 59,495, 61,494, 60,
>  502)( 67,714,469,508,432,496)( 68,497,189,430,517,422)( 72, 74)
> ( 76,219, 87,386,443,218)( 77,662, 92,118,447,598)( 78,213,600,240,648,
>  576)( 79,397,110,592, 80,212)( 81,239,607,216,112,486)( 82,170)
> ( 83,222,458,214,452,210)( 84,656, 85,223,385,228)( 88,657, 97,220,574,
>  116)( 89,523, 98,492,398,591)( 90,234,381,522,580,121)
> ( 91,232,584,500,101,499)( 93,226,103,503,413,524)( 94,225,104,505,113,
>  661)( 95,160, 96,158,105,162)( 99,493,107,593,114,479)
> (100,605,411,231,596,161)(102,126,145,122,146,119)(106,215,108,211,401,
>  227)(109,590,115,511,111,408)(117,149,125,377,554,247)
> (120,233,389,660,765,159)(123,382,664,763,230,390)(124,148,588,246,595,
>  573)(127,550,425,752,448,575)(128,551,142,393,135,249)
> (129,556,380,248,154,487)(130,392,133,621,144,157)(131,549,138,623,412,
>  597)(134,403,152,750,136,546)(137,171)(139,755,140,643,599,553)
> (143,601,147,655,379,156)(150,626,151,606,391,744)(153,501,387,610,155,
>  427)(195,471,205,632,275,642)(197,206,266,268,625,261)
> (198,293,207,483,200,637)(199,490,263,202,260,635)(203,712,509,269,279,
>  711)(204,529,274,267,651,459)(224,609,229,384,518,383)
> (235,346,680,348,442,702)(236,699,243,478,748,710)(237,244,352,354,698,
>  350)(238,757,747,344,245,603)(241,737,615,340,544,733)
> (242,672,488,673,652,353)(250,466,477,506,252,484)(251,259,347,311,400,
>  730)(253,257,295,258,297,693)(254,296)(255,306)(256,351)
> (262,283,624,620,271,485)(264,287,641)(265,421)(270,280,423,289,405,272
>  )(273,277,450,692,281,420)(276,634,282,716,290,653)(278,534,520,713,
>  533,525)(284,291,438,706,439,721)(285,374,292,451,638,644)
> (286,719,491,288,473,433)(294,715,645)(298,308,312,726,302,307)
> (299,666,314,568,303,327)(300,301,725,640,463,304)(305,332,456)
> (309,650,310,313,723,318)(315,355,325,417,367,510)(316,322,317,399,326,
>  409)(319,756,372,470,557,631)(320,602,361,694,369,410)(321,670,604)
> (323,683,519,687,686,608)(324,617,449,671,682,564)(328,370,538,696,732,
>  669)(329,378,337,675,331,416)(330,768,753,366,722,762)
> (333,558,678,717,742,559)(334,407,341,572,745,419)(335,414,356,613,746,
>  583)(336,561,582,758,679,362)(338,342,586,339,359,700)
> (343,736,740,728,585,555)(345,365,457)(349,667,639,761,751,707)
> (357,571,406)(358,663,690,658,734,541)(360,543,565,676,739,542)
> (363,735,371,684,364,418)(368,727,759,743,685,741)(396,514,567,579,566,
>  581)(402,513,616,426,545,766)(429,563,691,594,537,535)
> (431,704,647,708,720,453)(460,709,464,472,465,636)(468,633,646)
> (507,630,526,627,516,654)(521,689,540,539,764,570)(547,677,695,665,697,
>  729)(548,560)(562,754,578,674,681,731)(569,659)(577,668,587,738,589,
>  760)(618,701,724,688,749,703)(628,767)(649,718,705), (  1,  9, 85,514,
>  38,398,  3, 10,140,513,131, 57)(  2, 11, 41, 67,452,107)
> (  4,516,310,590,328,195)(  5,535,353,495,284,372, 73,521,459,610,362,
>  236)(  6,394,453,343,249,746,  7,163,562,293,218,282)(  8,395,741,344,
>  186,361)( 12, 46, 91,611,497, 93, 14,120,377,573,382, 48)
> ( 13, 90,373,596,383, 94)( 15,469, 89,127,454,447, 16,579, 45, 78,448,
>   34)( 17,426,114, 31,648,130)( 18,103,380,247,149, 39)
> ( 19, 55,607,208,101,138, 20,104,375,584, 53, 83)( 21,422,153,128, 51,
>   81, 22,390, 60, 76,147, 36)( 23,384,111, 29, 97,129)( 24, 98,379,246,
>  146, 40)( 25,467,574,441, 96,139, 26, 99,440,411, 50, 84)
> ( 27,250,116,374,307,123, 74,251, 62,735,197, 68)( 28,387,132, 59)
> ( 30,112,137,151, 33,413,133,154, 82, 58,443,113)( 32, 87,141,412, 35,
>  155,134,142, 86,475, 80,115)( 37,108,135,404, 77,461)( 42,458,136, 61,
>  79, 43)( 44, 92,580, 54,376,385)( 47,515,105,389,599,143,144,765,102,
>  381,444, 88)( 49,106)( 52,432,401,445,600,763)( 56, 95,150,145)
> ( 63,460,520,118,273,568)( 64,670,699,121,764,269,158,571,471, 65,526,
>  564)( 66,438,421,194,705,534,160,538,255,233,703,683)( 69,317,267,175,
>  320,652,124,450,309,177,276,650)( 70,708,466,517,720,633,499,743,258,
>  229,685,665)( 71,322,266,169,325,457,126,277,308,171,280,456)
> ( 72,295,156,378,237,518)( 75,109)(100,766,391,152,425,609,148,581,435,
>  110,424,430)(117,360,690,498,316,485,500,589,519,157,338,235)
> (119,645,470,159,594,340)(122,561,256,234,724,663)(125,681,259,230,731,
>  547)(161,586,673,176,356,651)(162,342,352,170,745,641)
> (164,355,541,588,583,509)(165,572,608,532,694,615,388,270,525,605,716,
>  682)(166,684,243,180,719,303,168,675,205,212,768,262)(167,451,557,546,
>  742,346)(172,602,238,178,647,305,174,613,200,210,759,264)
> (173,634,728,549,674,345)(179,718,265,598,669,241)(181,706,506,386,559,
>  245)(182,367,348,462,628,327)(183,428,740,224,366,490,215,629,483,189,
>  288,463)(184,371,349,455,630,726)(185,627,756,545,370,274,216,570,642,
>  508,291,318)(187,654,319,755,406,686,655,429,748,489,604,734)
> (188,439,304,567,722,268)(190,510,323,505,727,204,227,405,278,503,578,
>  242)(191,649,484,492,638,298)(192,418,620,240,678,478,595,416,442,201,
>  433,631)(193,417,529,223,542,737,554,419,672,434,636,671)
> (196,721,449,606,701,306,392,679,203,211,749,351)(198,530,363,347,402,
>  540)(199,397,653,646,501,739,639,437,410,697,408,587)(202,592,760,296,
>  494,369,707,750,543,254,511,335)(206,228,688,730,415,364,244,553,618,
>  257,493,331)(207,213,582,693,512,491,736,550,696,311,393,753)
> (209,285,477,496,507,555,614,329,297,396,563,747)(214,289,299,556,560,
>  680,597,334,624,239,659,283)(217,577,350,660,668,365,612,565,261,527,
>  472,332)(219,569,279,486,420,713)(220,689,275,656,294,533)
> (221,732,751,616,558,354,552,758,263,714,473,312)(222,539,625,576,292,
>  301,623,691,698,575,337,260)(225,692,468,591,272,252,226,339,695,593,
>  341,400)(231,644,666,752,762,632)(232,423,723,643,738,712)
> (248,537,710,566,336,488)(253,476,399,729,531,315)(271,524,359,711,657,
>  754)(281,617,601,368,702,481,326,733,528,431,314,661)(286,725,479,715,
>  585,621,717,667,446,321,757,619)(287,482,464,302,522,676)
> (290,300,622,709,480,427)(313,744,407,358,504,704)(324,487,700,658,551,
>  548,544,474,409,687,436,767)(330,635,523,357,637,662)(333,761,626,536,
>  603,664)(403,414,677,502,465,640) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Z(2)
Group
 | Z(3)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(2)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
 | Z(3)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 1088391168, 544195584, 181398528, 45349632, 22674816, 2519424, 839808, 
  13122, 6561, 1 ]

# $Suz$ on 1782 points
gap> g:=
> Group( (   2,   3)(   8,  14)(   9,  15)(  11,  17)(  13,  24)
> (  16,  25)(  18,  31)(  20,  28)(  23,  40)(  26,  29)(  27,  43)
> (  30,  54)(  32,  57)(  35,  48)(  36,  64)(  38,  68)(  39,  69)
> (  42,  49)(  44,  50)(  45,  77)(  46,  72)(  47,  73)(  51,  87)
> (  52,  91)(  53,  93)(  55,  96)(  56,  97)(  58, 101)(  60,  80)
> (  61,  81)(  62, 106)(  63, 109)(  65, 111)(  67, 114)(  71,  82)
> (  74,  84)(  75,  85)(  76, 124)(  78, 120)(  79, 119)(  86, 133)
> (  88, 138)(  89, 140)(  90, 144)(  92, 147)(  94, 149)(  95, 150)
> (  98, 125)(  99, 155)( 100, 158)( 102, 160)( 104, 129)( 105, 164)
> ( 107, 166)( 108, 168)( 110, 170)( 113, 174)( 115, 171)( 118, 130)
> ( 121, 131)( 122, 182)( 123, 183)( 126, 178)( 127, 187)( 128, 177)
> ( 132, 191)( 134, 153)( 135, 195)( 136, 198)( 137, 201)( 139, 203)
> ( 141, 204)( 142, 208)( 143, 210)( 145, 213)( 146, 214)( 148, 217)
> ( 151, 184)( 154, 223)( 156, 225)( 157, 227)( 159, 229)( 162, 189)
> ( 163, 233)( 165, 235)( 167, 239)( 169, 241)( 172, 244)( 173, 246)
> ( 175, 242)( 179, 251)( 180, 190)( 181, 254)( 185, 249)( 186, 260)
> ( 188, 248)( 192, 220)( 193, 267)( 194, 270)( 196, 273)( 197, 275)
> ( 199, 277)( 200, 279)( 202, 281)( 205, 285)( 206, 283)( 207, 288)
> ( 209, 292)( 211, 295)( 212, 296)( 215, 282)( 216, 256)( 218, 257)
> ( 222, 306)( 224, 308)( 226, 311)( 228, 313)( 230, 315)( 231, 263)
> ( 232, 319)( 234, 321)( 236, 299)( 237, 325)( 238, 328)( 240, 331)
> ( 243, 334)( 245, 336)( 247, 332)( 250, 342)( 252, 264)( 253, 347)
> ( 255, 343)( 258, 340)( 259, 355)( 261, 357)( 262, 359)( 265, 303)
> ( 266, 363)( 268, 366)( 269, 368)( 271, 371)( 272, 365)( 274, 374)
> ( 276, 376)( 278, 380)( 280, 382)( 284, 387)( 286, 385)( 287, 391)
> ( 289, 377)( 290, 344)( 291, 397)( 293, 401)( 294, 402)( 297, 383)
> ( 298, 349)( 300, 384)( 301, 409)( 305, 413)( 307, 415)( 309, 418)
> ( 310, 422)( 312, 425)( 314, 427)( 316, 429)( 317, 432)( 318, 435)
> ( 320, 438)( 322, 405)( 323, 442)( 324, 446)( 326, 449)( 327, 450)
> ( 329, 453)( 330, 448)( 333, 458)( 335, 461)( 337, 462)( 338, 455)
> ( 339, 456)( 341, 468)( 345, 472)( 346, 474)( 348, 469)( 350, 372)
> ( 351, 394)( 352, 481)( 353, 466)( 354, 485)( 356, 487)( 358, 426)
> ( 360, 491)( 361, 493)( 362, 495)( 364, 498)( 367, 500)( 369, 503)
> ( 370, 497)( 373, 507)( 375, 509)( 378, 513)( 379, 516)( 381, 519)
> ( 386, 524)( 388, 527)( 389, 483)( 390, 530)( 392, 510)( 393, 470)
> ( 395, 408)( 396, 536)( 398, 540)( 399, 538)( 400, 543)( 403, 520)
> ( 404, 476)( 406, 521)( 407, 551)( 411, 554)( 412, 557)( 414, 560)
> ( 416, 563)( 417, 567)( 419, 570)( 420, 573)( 421, 575)( 423, 578)
> ( 424, 569)( 428, 583)( 430, 586)( 431, 588)( 433, 593)( 434, 594)
> ( 436, 597)( 437, 591)( 439, 546)( 440, 604)( 441, 608)( 443, 611)
> ( 444, 596)( 445, 614)( 447, 617)( 451, 620)( 452, 616)( 454, 618)
> ( 457, 492)( 459, 627)( 460, 626)( 463, 631)( 464, 632)( 465, 471)
> ( 467, 638)( 473, 643)( 475, 639)( 477, 504)( 478, 533)( 479, 580)
> ( 480, 653)( 482, 656)( 484, 659)( 486, 662)( 488, 582)( 489, 666)
> ( 490, 667)( 494, 673)( 496, 676)( 501, 679)( 502, 675)( 505, 683)
> ( 506, 686)( 508, 689)( 511, 692)( 512, 561)( 514, 696)( 515, 610)
> ( 517, 698)( 518, 562)( 522, 703)( 523, 705)( 525, 708)( 526, 711)
> ( 528, 714)( 529, 715)( 531, 690)( 532, 640)( 534, 550)( 535, 706)
> ( 537, 725)( 539, 727)( 541, 635)( 542, 731)( 544, 728)( 545, 645)
> ( 547, 700)( 548, 701)( 549, 741)( 552, 744)( 553, 748)( 555, 752)
> ( 556, 753)( 558, 756)( 559, 750)( 564, 764)( 565, 598)( 566, 768)
> ( 568, 771)( 572, 777)( 574, 779)( 576, 781)( 577, 770)( 579, 772)
> ( 581, 785)( 584, 787)( 585, 791)( 587, 795)( 589, 796)( 590, 799)
> ( 592, 801)( 595, 805)( 599, 802)( 600, 733)( 601, 710)( 602, 707)
> ( 603, 815)( 605, 818)( 606, 806)( 607, 822)( 609, 825)( 612, 804)
> ( 613, 829)( 615, 831)( 619, 830)( 621, 832)( 622, 833)( 623, 834)
> ( 624, 840)( 625, 841)( 628, 842)( 629, 827)( 630, 843)( 633, 852)
> ( 634, 849)( 636, 855)( 637, 856)( 641, 860)( 642, 861)( 644, 862)
> ( 646, 680)( 647, 859)( 648, 718)( 649, 746)( 650, 760)( 651, 873)
> ( 652, 759)( 654, 876)( 655, 877)( 657, 702)( 658, 881)( 660, 878)
> ( 661, 886)( 663, 786)( 664, 755)( 665, 890)( 668, 895)( 669, 898)
> ( 670, 899)( 672, 903)( 674, 905)( 678, 907)( 681, 912)( 682, 814)
> ( 684, 917)( 685, 824)( 687, 919)( 688, 762)( 691, 743)( 693, 925)
> ( 694, 926)( 695, 927)( 697, 929)( 699, 928)( 704, 937)( 709, 942)
> ( 712, 946)( 713, 947)( 716, 948)( 717, 858)( 719, 921)( 720, 737)
> ( 721, 722)( 723, 961)( 724, 962)( 726, 965)( 729, 932)( 730, 970)
> ( 732, 971)( 734, 968)( 735, 969)( 736, 980)( 738, 933)( 739, 934)
> ( 740, 987)( 742, 788)( 745, 994)( 747, 897)( 749, 998)( 751,1000)
> ( 754,1003)( 757, 766)( 758,1001)( 761,1009)( 763,1011)( 767,1015)
> ( 769,1017)( 775,1023)( 776,1024)( 778,1026)( 780,1016)( 782,1018)
> ( 783,1019)( 784,1032)( 789,1034)( 790,1013)( 792,1039)( 793,1042)
> ( 794,1043)( 797,1046)( 798,1047)( 800,1050)( 803,1055)( 807,1048)
> ( 808,1052)( 809,1053)( 810, 943)( 811,1065)( 812,1066)( 813,1069)
> ( 816,1073)( 817,1074)( 820,1056)( 821,1081)( 823,1082)( 826,1075)
> ( 828,1086)( 835,1088)( 836,1089)( 837,1090)( 838, 944)( 839,1091)
> ( 844,1033)( 845,1079)( 846,1099)( 847,1101)( 848,1106)( 850,1109)
> ( 851,1111)( 853,1113)( 854,1114)( 857,1115)( 863,1116)( 864,1127)
> ( 865,1128)( 866,1135)( 867, 909)( 868,1122)( 869, 955)( 870, 990)
> ( 871,1140)( 872,1141)( 874,1031)( 875,1144)( 879,1151)( 880,1152)
> ( 882,1145)( 883,1154)( 884,1149)( 885,1160)( 887,1004)( 888,1163)
> ( 889,1164)( 891,1165)( 892, 894)( 893,1098)( 896, 959)( 902,1178)
> ( 904,1179)( 906,1181)( 908, 924)( 910, 991)( 911,1063)( 913,1187)
> ( 914,1068)( 915,1189)( 916,1190)( 918,1192)( 920,1191)( 922,1197)
> ( 923, 988)( 930,1199)( 931,1198)( 935,1208)( 936,1209)( 938,1210)
> ( 939,1213)( 940,1214)( 941,1136)( 945,1219)( 949,1195)( 950,1220)
> ( 951,1118)( 952,1224)( 953,1225)( 954,1234)( 956,1196)( 957, 981)
> ( 958,1240)( 960,1242)( 963,1243)( 964, 967)( 966,1248)( 972,1260)
> ( 973,1257)( 974,1258)( 975,1265)( 976,1254)( 977,1270)( 978,1085)
> ( 979,1273)( 982,1279)( 983,1206)( 984,1100)( 985,1207)( 986,1237)
> ( 989,1020)( 992,1287)( 993,1288)( 995,1291)( 996,1292)( 997,1293)
> ( 999,1296)(1002,1300)(1005,1294)(1006,1298)(1007,1027)(1008,1305)
> (1010,1307)(1012,1306)(1014,1289)(1022,1035)(1025,1314)(1028,1310)
> (1029,1311)(1030,1255)(1036,1319)(1037,1320)(1038,1078)(1040,1326)
> (1041,1327)(1044,1051)(1045,1328)(1049,1334)(1054,1338)(1057,1330)
> (1058,1332)(1059,1333)(1060,1076)(1061,1336)(1062,1217)(1064,1349)
> (1070,1355)(1071,1356)(1072,1357)(1080,1361)(1083,1095)(1084,1096)
> (1087,1329)(1092,1365)(1093,1366)(1094,1218)(1097,1227)(1102,1379)
> (1103,1174)(1104,1171)(1105,1384)(1107,1386)(1108,1387)(1110,1388)
> (1112,1390)(1117,1392)(1119,1393)(1120,1394)(1121,1403)(1123,1147)
> (1124,1126)(1125,1173)(1129,1416)(1130,1419)(1131,1412)(1132,1424)
> (1133,1414)(1134,1428)(1137,1404)(1138,1236)(1139,1431)(1142,1432)
> (1143,1148)(1146,1441)(1150,1271)(1153,1447)(1155,1439)(1156,1158)
> (1157,1457)(1159,1460)(1161,1461)(1162,1464)(1166,1376)(1167,1466)
> (1168,1377)(1169,1374)(1170,1375)(1172,1473)(1175,1477)(1177,1479)
> (1180,1186)(1182,1481)(1183,1346)(1184,1368)(1185,1284)(1188,1484)
> (1193,1485)(1194,1483)(1200,1308)(1201,1343)(1202,1304)(1203,1435)
> (1204,1499)(1205,1502)(1211,1448)(1212,1508)(1215,1511)(1216,1223)
> (1221,1350)(1222,1506)(1226,1519)(1228,1530)(1229,1533)(1230,1525)
> (1231,1538)(1232,1520)(1233,1542)(1235,1546)(1238,1491)(1239,1276)
> (1241,1552)(1244,1554)(1245,1555)(1246,1556)(1247,1563)(1249,1256)
> (1250,1564)(1251,1565)(1252,1425)(1253,1462)(1259,1532)(1261,1580)
> (1262,1575)(1263,1582)(1264,1509)(1266,1584)(1267,1536)(1268,1363)
> (1269,1274)(1272,1586)(1275,1588)(1277,1589)(1278,1562)(1280,1503)
> (1281,1318)(1282,1548)(1283,1587)(1285,1590)(1286,1591)(1290,1297)
> (1295,1492)(1299,1570)(1301,1594)(1302,1597)(1303,1598)(1309,1372)
> (1313,1321)(1315,1606)(1316,1504)(1317,1572)(1322,1610)(1323,1352)
> (1324,1360)(1325,1613)(1331,1617)(1335,1359)(1337,1524)(1339,1615)
> (1340,1616)(1341,1358)(1342,1618)(1344,1539)(1345,1609)(1347,1627)
> (1348,1480)(1353,1629)(1354,1630)(1362,1369)(1364,1614)(1367,1397)
> (1370,1633)(1371,1518)(1373,1527)(1378,1642)(1380,1644)(1381,1472)
> (1382,1649)(1383,1652)(1385,1654)(1389,1655)(1391,1653)(1395,1663)
> (1396,1658)(1398,1456)(1399,1422)(1400,1660)(1401,1668)(1402,1498)
> (1405,1442)(1406,1443)(1407,1662)(1408,1474)(1409,1475)(1410,1415)
> (1411,1559)(1413,1676)(1417,1426)(1418,1679)(1420,1681)(1421,1684)
> (1423,1476)(1427,1568)(1429,1526)(1430,1547)(1433,1689)(1434,1592)
> (1436,1687)(1437,1688)(1438,1693)(1440,1540)(1444,1500)(1445,1450)
> (1446,1571)(1449,1694)(1451,1529)(1452,1455)(1453,1458)(1454,1700)
> (1459,1702)(1463,1705)(1465,1596)(1467,1638)(1468,1707)(1469,1639)
> (1470,1636)(1471,1637)(1478,1718)(1482,1635)(1486,1604)(1487,1622)
> (1488,1620)(1489,1722)(1490,1726)(1493,1605)(1494,1573)(1495,1514)
> (1496,1600)(1497,1599)(1501,1603)(1505,1507)(1510,1667)(1512,1551)
> (1513,1714)(1515,1733)(1516,1734)(1517,1737)(1521,1730)(1522,1731)
> (1523,1680)(1528,1739)(1531,1717)(1534,1576)(1535,1632)(1537,1543)
> (1541,1696)(1544,1741)(1545,1743)(1549,1558)(1550,1656)(1553,1685)
> (1557,1648)(1560,1736)(1561,1746)(1566,1692)(1567,1645)(1569,1704)
> (1574,1748)(1577,1701)(1578,1669)(1579,1754)(1581,1756)(1583,1695)
> (1585,1758)(1593,1686)(1595,1720)(1601,1760)(1602,1755)(1607,1611)
> (1608,1728)(1612,1628)(1619,1690)(1621,1763)(1623,1631)(1624,1761)
> (1626,1719)(1634,1664)(1640,1682)(1641,1769)(1643,1677)(1646,1713)
> (1647,1703)(1650,1651)(1657,1715)(1659,1683)(1661,1698)(1665,1699)
> (1666,1742)(1670,1768)(1671,1774)(1672,1711)(1673,1675)(1674,1776)
> (1678,1727)(1691,1759)(1697,1738)(1706,1750)(1708,1753)(1709,1778)
> (1710,1773)(1712,1757)(1716,1777)(1723,1729)(1724,1765)(1725,1764)
> (1732,1775)(1735,1747)(1740,1752)(1744,1749)(1745,1772)(1751,1779)
> (1770,1771), (   1,   5,  39, 386, 390, 490, 688, 452, 414, 315, 800,
>   902, 628, 823, 557, 448, 245, 709, 205,  51,  11)(   3,  73, 640,
>   715, 644,1750, 792, 756,1131, 409, 144, 439,1318, 836, 226,1260,1394,
>  734, 182,  31,   6)(   4,  34, 128, 717,1604, 722,1341,1627,1009, 232,
>  461,1136,1501,1640, 834,1409, 973, 171, 550,  30,  42)(   7, 257, 219,
>  260, 680, 659, 732,1089, 766,1256, 857,1671, 703, 600, 878,1531,1457,
>  1741,1266, 977,  52)(   8,  69, 259, 824, 574, 625, 880,1072, 993,
>   608, 569, 316, 940, 338, 605,1178, 960,1064, 757, 156,  20)
> (   9,  22, 532, 421,1244,1381,1559,1335, 465,1099, 714,1436, 667, 602,
>  1389, 966,1752,1638, 430, 111,  29)(  10,  15,  47,  82, 356, 718,
>   881, 623, 979, 971,1736,1442, 666, 762, 919,1484, 925, 352,1051,1231,
>  89)(  12, 393, 274, 929, 725, 885, 809, 736,1392,1776, 870, 892, 566,
>  1203, 984,1774,1161, 802, 952, 251,  90)(  13, 132, 113, 575, 633,
>   598, 107)(  14,  61, 162, 450, 568, 482, 433,1477, 872, 293, 624,
>   822, 770,1080, 997, 784, 704,1184, 380, 196,  56)(  16, 118, 103,
>   805,1294,1474, 631, 607, 578,1410,1713, 649,1433,1468,1058, 305, 583,
>  1066,1333, 783,  99)(  17,  81,  70, 114, 247, 610, 329, 555,1324,
>  1482, 695,1038,1518, 761,1479, 992, 507, 268, 145,  48,  41)
> (  18, 130, 486,1281,1706,1400, 408)(  19,  79, 192, 178, 509,1549,
>  1737,1084, 172,1195,1255,1378,1502, 359,1017,1252,1513, 343,  63, 220,
>  141)(  21, 498, 475, 685,1319,1304, 899, 701,1695,1561, 621,1355, 926,
>  1696,1337, 982, 682,1465,1173,1643, 458)(  23, 284,  86,  67, 374,
>   272, 165)(  24, 148, 189, 523, 936, 346,1045,1626, 906, 195, 224,
>    35, 104, 227, 918,1607, 694, 726, 400, 935, 142)(  25, 218, 185,
>  1314,1062, 742,1174, 957,1703, 588,1623,1767,1027,1739,1085, 866,1402,
>  1380,1100, 622,  62)(  26, 265, 249, 781,1565, 891,1757, 799, 309,
>  1101,1264,1149, 785,1670,1692, 728,1606, 827, 584, 967, 377)
> (  27,  49, 303, 206, 161,1082,1302, 494,1146,1421,1598, 987,1440,1664,
>  1274,1382,1336,1406, 864, 147, 154)(  28, 176, 341, 753, 616, 999,
>  1177, 518, 330,  65,  32, 116, 174, 658,1041, 422, 665, 806, 312, 730,
>  92)(  33, 308, 295, 434,1464, 896, 846, 445,1725, 692,1361, 691,1163,
>  1650,1254, 604, 863,1738,1129,1545, 358)(  36, 153,  75, 662,1430,
>   683, 774, 611,1233, 862,1742,1374, 942,1157,1678,1063,1164,1473,1102,
>  1710, 808)(  37, 676,1207,1095,1012, 399, 920,1248, 893, 444,1036,
>  1345, 930,1220,1446, 262,1015, 472, 344, 254,  54)(  38, 275, 502,
>   778, 724, 798,1718, 924, 804, 763, 673, 851,1013, 328, 419, 634, 122,
>  223, 375, 777, 335)(  40, 186, 368, 595, 755, 888, 812,1182, 460,1033,
>  767, 636, 337, 596, 564, 101, 271,  95, 129,  76, 207)(  43, 470, 347,
>  340,1595, 842,1216,1634,1340,1068,1761, 499, 890,1768,1338, 536,1614,
>  1204,1423, 384, 105)(  44, 487, 720, 985,1758,1753, 586, 449, 954,
>  1115,1732,1672,1777,1701,1633,1079,1512,1646,1544, 215, 510)
> (  45, 123, 287, 246, 945, 463,  80)(  46, 134,  53,  71,  59, 415,
>   856, 544,1699,1259,1243,1475,1271,1253,1196,1147,1560, 710, 453,1019,
>  314)(  50, 119, 476, 530,1754,1251,1581,1667, 933, 601, 336, 388,1686,
>  1746,1663,1416,1532,1439,1190, 136, 170)(  55,  83,  94, 117, 250,
>   495, 754, 845, 687,1478, 514,1112, 459, 712, 797,1347,1020, 239, 443,
>  64, 110)(  57, 191, 391, 556,1111,1213,1685,1401, 120, 376, 403,1404,
>   491,1771,1438, 909,1227,1375, 801,1537, 350)(  58, 298, 157,1118,
>   976, 394, 242, 737, 258,1622, 772,1114,1444,1659,1711,1059, 813,1609,
>  571, 825,1006)(  60, 158, 369, 467,1110,1008,1325, 567, 139, 201, 675,
>  1025,1070,1625, 874, 319, 830, 889,1078, 573, 428)(  66,1003,1422,
>   548,1516,1662, 735,1575,1093,1635,1781, 378,1653, 963,1138, 814,1176,
>  931, 135,  98,  93)(  68, 175, 168, 697,1175, 267, 364, 211, 263, 713,
>  944, 435, 424, 102, 212, 253, 594, 577, 674, 875, 489)(  72, 349, 133,
>  288, 362, 883,1534,1061,  84, 235, 150, 342, 143, 112,1307,1414,1316,
>  1775, 938, 833, 243)(  74, 229, 180, 620,1311, 612,1322,1624, 699,
>  1125,1769,1644,1572,1328,1005, 479, 261, 533, 332,1547,1132)
> (  77, 302, 355,1280,1760,1242,1432,1092, 310,1391,1167,1510,1407,1472,
>  585, 560,1450,1687, 795,1230, 300)(  78, 281, 700, 572, 964,1569,1159)
> (  85, 177, 951,1676,1602,1759, 660,1272,1454, 292,1448,1498,1702,1039,
>  1011,1128, 839, 214, 406, 124, 221)(  87, 183, 304, 204, 184, 152,
>   217, 468, 466,1720,1240,1592,1571, 986,1142, 955,1397,1587,1043, 471,
>  256)(  88, 371, 741, 353,1620,1719, 927)(  91, 322, 648, 776,1765,
>   561,1077, 519, 656,1279, 837,1371,1782, 512, 972, 599, 291,1689,1107,
>  1236,1262)(  96, 387, 520, 483,1617,1197, 898,1044, 716,1668,1155,
>   455,1460,1458,1726, 535,1334,1288, 541, 299, 477)(  97, 149, 524,
>  1558,1310, 961,1636,1419, 739,1690,1104, 947, 395, 469, 108, 858,1156,
>  1637, 593, 323, 166)( 100, 404, 327,1596,1428, 456, 831,1497, 481,
>  1194, 193, 405, 646, 485,1700, 969,1594,1250, 838, 396, 216)
> ( 106, 159, 294, 529,1186, 629, 850, 941, 996,1035, 473, 360, 437, 326,
>  537, 146, 181, 306, 576, 939, 587)( 109, 169, 354, 816,1323,1762, 989,
>  464, 590,1611,1007, 427, 769, 654, 592, 539,1218, 516, 240, 641, 115)
> ( 121, 313, 389,1483,1305,1054, 953,1424, 884, 285, 383, 190,1026, 397,
>  1487,1309, 230,1350,1083, 552, 160)( 125, 410, 283, 886,1723,1443,
>  1540,1339, 412,1086, 998, 488, 829, 752, 441, 425,1520,1704,1398,1463,
>  140)( 126, 382,1282,1434, 255, 194, 151)( 127, 270, 307, 231, 614,
>   381,1313, 563, 780, 904,1353,1766, 693, 138, 497, 280,1024,1014, 854,
>  817, 642)( 131, 321, 638,1577,1246,1494,1453,1533,1553,1586,1121,1120,
>  1751,1119, 208, 266, 546,1503, 426,1223, 282)( 137, 503,1491,1030,
>  1666,1500, 351)( 155, 276, 233, 451, 749,1321, 745)( 163, 248,1221,
>  1683,1618, 554, 847,1511,1717, 835,1629, 696, 865,1747,1680, 868,1368,
>  914, 677, 203, 521)( 164, 228, 484,1348,1004, 508,1022, 325, 436, 559,
>  447,1354,1023, 542, 913, 198, 370, 234, 173, 768, 199)( 167,1116,1705,
>  1370,1141,1127, 937,1342,1299,1232,1601, 672,1722, 513,1021, 570,1228,
>  1418, 603,1312,1202)( 179, 363, 496, 637,1286, 686, 501, 655, 684,
>   958, 811, 334, 615,1188, 907,1241,1071,1612,1780,1181, 651)
> ( 187, 504, 402,1548,1526,1578,1661, 522,1193,1605, 820,1295, 663,1514,
>  1258,1708,1654,1042, 579, 841,1212)( 188, 949,1437,1270,1681, 897,
>  1435,1135,1171, 606,1002, 324,1631, 759, 429, 526,1049, 416, 225, 213,
>  222)( 197, 241, 286, 668,1656,1665, 209, 630,1550,1273,1426,1566,1527,
>  1429,1379, 707, 645,1455,1377, 525, 290)( 200,1192,1630,1031, 492,
>   236, 478)( 202, 279, 365)( 210,1154,1268, 740,1745, 990,1191,1645,
>   796,1764,1721, 908,1134,1515,1073, 379,1037,1489, 511, 273, 551)
> ( 237, 932,1123,1642,1779, 882,1261,1573,1466,1731, 848,1712,1431,1277,
>  289, 392, 531,1137,1187, 480, 803)( 238,1297,1528, 252,1331, 562, 689,
>  876,1649,1486,1564,1327, 782, 877, 934,1075,1224,1349,1600, 635,1076)
> ( 244, 613,1352, 775, 446, 517,1360, 500, 828,1628, 678, 786,1010, 903,
>  1162, 853, 871, 995,1040, 418, 320)( 264,1343,1525, 815,1290, 950,
>  1130, 832,1000,1445, 719,1682,1582,1028,1144, 983,1615,1287,1675,1451,
>  1697)( 269, 661,1145,1535, 681, 366, 348)( 277, 297, 690, 385,1211,
>   807,1217,1199,1267, 911, 679, 580,1507, 980,1385, 840, 708,1655,1568,
>  440, 900)( 278,1034,1300, 965,1091, 627,1749,1563,1090, 750,1320,1492,
>  1390,1517, 981,1150, 974,1048,1306,1519,1356)( 296, 547, 705,1608,
>  1189,1597,1552,1772,1652,1363, 339,1081, 744, 617,1570, 457,1505,1117,
>  975,1269, 372)( 301, 407, 549,1238,1733,1291,1168,1651,1529,1105,1660,
>  1263,1160,1411,1469,1603, 912,1387, 721,1060, 727)( 311, 609, 413,
>  1016,1108, 723, 793)( 317, 671, 852,1744,1694,1292, 626,1050, 860,
>  1506,1098, 591,1185,1551,1546,1096, 540,1283,1180,1427,1585)
> ( 318,1289, 538, 545,1362, 743, 905, 760,1364,1493, 873,1490,1425, 647,
>  1357,1298, 731,1359,1234,1245, 818)( 331,1225,1330,1200,1408,1209,
>   968,1065,1538,1756, 991,1179,1346, 988,1151,1583,1366, 664, 789,1724,
>  652)( 333,1495, 867,1265,1470,1580,1206)( 345, 894, 946,1557,1413,
>   657,1358, 420,1103,1057,1183, 928,1673, 702, 357, 534, 639, 515,1284,
>  1441, 826)( 361,1329,1496,1530,1693,1405,1208,1459,1393,1152,1303,
>  1688,1369,1308, 959,1485,1018,1113,1170,1046, 758)( 367, 879,1714,
>  1632,1122, 462,1778,1555,1140,1471,1590,1647,1166,1219, 738,1462,1278,
>  943, 779, 493,1488)( 373, 787,1126,1727,1734,1728,1388,1399, 618, 855,
>  1210,1677,1584, 747, 765, 597,1001,1226, 401,1616,1029)
> ( 398,1139, 581, 528,1285, 916, 790)( 411, 901, 771,1476,1684,1169,
>  1214,1257,1613, 553, 819, 698, 849,1621,1599,1415, 978,1367, 956,1588,
>  1326)( 417,1148,1239,1589,1344,1658,1047)( 423,1172, 794, 442, 619,
>   558,1056)( 431,1067, 788,1249,1053,1574,1639,1735,1576, 589,1351,
>   923,1657,1556,1730,1591,1567,1052, 643,1447,1740)( 432, 729,1691,
>  1396, 474,1395,1235, 505,1554,1743,1539, 910,1109,1773,1158,1403,1376,
>  565,1124,1679,1619)( 438,1543,1648,1755,1237,1229,1524, 921,1509,1386,
>  1315, 506,1610,1198,1032,1449, 543,1521,1094,1069, 773)
> ( 454, 962,1205,1275,1480,1499, 669,1593,1106, 711, 843,1770, 746,1087,
>  1372, 632,1562,1317, 917,1133,1716)( 527,1201, 948,1365, 887,1715,1165
>  )( 582, 844, 821, 751, 670, 915, 922)( 650, 733,1522,1420,1332, 994,
>  1536, 859,1074,1542,1669,1247,1276,1088,1293,1412,1373,1763, 748,1143,
>  1301)( 653, 895,1709, 791, 764,1541,1579)( 706,1055, 861,1504,1641,
>  1508,1481)( 810,1296, 970,1698,1523,1215, 869)(1097,1456,1383,1461,
>  1467,1748,1153)(1222,1674,1384,1729,1707,1452,1417) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | Suz
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 448345497600, 1 ]

# test
gap> g:= 
> Group( (  1,  5,  7,  3, 12, 24, 11)(  2, 23,  4, 27, 13, 14, 26)
> (  6, 20, 18,  8, 25, 21, 28)(  9, 10, 17, 15, 22, 16, 19)
> ( 29, 33, 35, 31, 40, 52, 39)( 30, 51, 32, 55, 41, 42, 54)
> ( 34, 48, 46, 36, 53, 49, 56)( 37, 38, 45, 43, 50, 44, 47)
> ( 57, 61, 63, 59, 68, 80, 67)( 58, 79, 60, 83, 69, 70, 82)
> ( 62, 76, 74, 64, 81, 77, 84)( 65, 66, 73, 71, 78, 72, 75)
> ( 85, 89, 91, 87, 96,108, 95)( 86,107, 88,111, 97, 98,110)
> ( 90,104,102, 92,109,105,112)( 93, 94,101, 99,106,100,103)
> (113,117,119,115,124,136,123)(114,135,116,139,125,126,138)
> (118,132,130,120,137,133,140)(121,122,129,127,134,128,131)
> (141,145,147,143,152,164,151)(142,163,144,167,153,154,166)
> (146,160,158,148,165,161,168)(149,150,157,155,162,156,159)
> (169,173,175,171,180,192,179)(170,191,172,195,181,182,194)
> (174,188,186,176,193,189,196)(177,178,185,183,190,184,187)
> (197,201,203,199,208,220,207)(198,219,200,223,209,210,222)
> (202,216,214,204,221,217,224)(205,206,213,211,218,212,215)
> (225,229,231,227,236,248,235)(226,247,228,251,237,238,250)
> (230,244,242,232,249,245,252)(233,234,241,239,246,240,243)
> (253,257,259,255,264,276,263)(254,275,256,279,265,266,278)
> (258,272,270,260,277,273,280)(261,262,269,267,274,268,271)
> (281,285,287,283,292,304,291)(282,303,284,307,293,294,306)
> (286,300,298,288,305,301,308)(289,290,297,295,302,296,299)
> (309,313,315,311,320,332,319)(310,331,312,335,321,322,334)
> (314,328,326,316,333,329,336)(317,318,325,323,330,324,327)
> (337,341,343,339,348,360,347)(338,359,340,363,349,350,362)
> (342,356,354,344,361,357,364)(345,346,353,351,358,352,355)
> (365,369,371,367,376,388,375)(366,387,368,391,377,378,390)
> (370,384,382,372,389,385,392)(373,374,381,379,386,380,383)
> (393,397,399,395,404,416,403)(394,415,396,419,405,406,418)
> (398,412,410,400,417,413,420)(401,402,409,407,414,408,411)
> (421,425,427,423,432,444,431)(422,443,424,447,433,434,446)
> (426,440,438,428,445,441,448)(429,430,437,435,442,436,439)
> (449,453,455,451,460,472,459)(450,471,452,475,461,462,474)
> (454,468,466,456,473,469,476)(457,458,465,463,470,464,467)
> (477,481,483,479,488,500,487)(478,499,480,503,489,490,502)
> (482,496,494,484,501,497,504)(485,486,493,491,498,492,495)
> (505,509,511,507,516,528,515)(506,527,508,531,517,518,530)
> (510,524,522,512,529,525,532)(513,514,521,519,526,520,523)
> (533,537,539,535,544,556,543)(534,555,536,559,545,546,558)
> (538,552,550,540,557,553,560)(541,542,549,547,554,548,551)
> (561,565,567,563,572,584,571)(562,583,564,587,573,574,586)
> (566,580,578,568,585,581,588)(569,570,577,575,582,576,579)
> (589,593,595,591,600,612,599)(590,611,592,615,601,602,614)
> (594,608,606,596,613,609,616)(597,598,605,603,610,604,607)
> (617,621,623,619,628,640,627)(618,639,620,643,629,630,642)
> (622,636,634,624,641,637,644)(625,626,633,631,638,632,635)
> (645,649,651,647,656,668,655)(646,667,648,671,657,658,670)
> (650,664,662,652,669,665,672)(653,654,661,659,666,660,663)
> (673,677,679,675,684,696,683)(674,695,676,699,685,686,698)
> (678,692,690,680,697,693,700)(681,682,689,687,694,688,691)
> (701,705,707,703,712,724,711)(702,723,704,727,713,714,726)
> (706,720,718,708,725,721,728)(709,710,717,715,722,716,719)
> (729,733,735,731,740,752,739)(730,751,732,755,741,742,754)
> (734,748,746,736,753,749,756)(737,738,745,743,750,744,747)
> (757,761,763,759,768,780,767)(758,779,760,783,769,770,782)
> (762,776,774,764,781,777,784)(765,766,773,771,778,772,775), 
> (  1,113,169, 57,309,645,281)(  2,114,170, 58,310,646,282)
> (  3,115,171, 59,311,647,283)(  4,116,172, 60,312,648,284)
> (  5,117,173, 61,313,649,285)(  6,118,174, 62,314,650,286)
> (  7,119,175, 63,315,651,287)(  8,120,176, 64,316,652,288)
> (  9,121,177, 65,317,653,289)( 10,122,178, 66,318,654,290)
> ( 11,123,179, 67,319,655,291)( 12,124,180, 68,320,656,292)
> ( 13,125,181, 69,321,657,293)( 14,126,182, 70,322,658,294)
> ( 15,127,183, 71,323,659,295)( 16,128,184, 72,324,660,296)
> ( 17,129,185, 73,325,661,297)( 18,130,186, 74,326,662,298)
> ( 19,131,187, 75,327,663,299)( 20,132,188, 76,328,664,300)
> ( 21,133,189, 77,329,665,301)( 22,134,190, 78,330,666,302)
> ( 23,135,191, 79,331,667,303)( 24,136,192, 80,332,668,304)
> ( 25,137,193, 81,333,669,305)( 26,138,194, 82,334,670,306)
> ( 27,139,195, 83,335,671,307)( 28,140,196, 84,336,672,308)
> ( 29,617, 85,729,337,365,701)( 30,618, 86,730,338,366,702)
> ( 31,619, 87,731,339,367,703)( 32,620, 88,732,340,368,704)
> ( 33,621, 89,733,341,369,705)( 34,622, 90,734,342,370,706)
> ( 35,623, 91,735,343,371,707)( 36,624, 92,736,344,372,708)
> ( 37,625, 93,737,345,373,709)( 38,626, 94,738,346,374,710)
> ( 39,627, 95,739,347,375,711)( 40,628, 96,740,348,376,712)
> ( 41,629, 97,741,349,377,713)( 42,630, 98,742,350,378,714)
> ( 43,631, 99,743,351,379,715)( 44,632,100,744,352,380,716)
> ( 45,633,101,745,353,381,717)( 46,634,102,746,354,382,718)
> ( 47,635,103,747,355,383,719)( 48,636,104,748,356,384,720)
> ( 49,637,105,749,357,385,721)( 50,638,106,750,358,386,722)
> ( 51,639,107,751,359,387,723)( 52,640,108,752,360,388,724)
> ( 53,641,109,753,361,389,725)( 54,642,110,754,362,390,726)
> ( 55,643,111,755,363,391,727)( 56,644,112,756,364,392,728)
> (141,533,477,197,673,561,757)(142,534,478,198,674,562,758)
> (143,535,479,199,675,563,759)(144,536,480,200,676,564,760)
> (145,537,481,201,677,565,761)(146,538,482,202,678,566,762)
> (147,539,483,203,679,567,763)(148,540,484,204,680,568,764)
> (149,541,485,205,681,569,765)(150,542,486,206,682,570,766)
> (151,543,487,207,683,571,767)(152,544,488,208,684,572,768)
> (153,545,489,209,685,573,769)(154,546,490,210,686,574,770)
> (155,547,491,211,687,575,771)(156,548,492,212,688,576,772)
> (157,549,493,213,689,577,773)(158,550,494,214,690,578,774)
> (159,551,495,215,691,579,775)(160,552,496,216,692,580,776)
> (161,553,497,217,693,581,777)(162,554,498,218,694,582,778)
> (163,555,499,219,695,583,779)(164,556,500,220,696,584,780)
> (165,557,501,221,697,585,781)(166,558,502,222,698,586,782)
> (167,559,503,223,699,587,783)(168,560,504,224,700,588,784)
> (225,253,449,393,589,421,505)(226,254,450,394,590,422,506)
> (227,255,451,395,591,423,507)(228,256,452,396,592,424,508)
> (229,257,453,397,593,425,509)(230,258,454,398,594,426,510)
> (231,259,455,399,595,427,511)(232,260,456,400,596,428,512)
> (233,261,457,401,597,429,513)(234,262,458,402,598,430,514)
> (235,263,459,403,599,431,515)(236,264,460,404,600,432,516)
> (237,265,461,405,601,433,517)(238,266,462,406,602,434,518)
> (239,267,463,407,603,435,519)(240,268,464,408,604,436,520)
> (241,269,465,409,605,437,521)(242,270,466,410,606,438,522)
> (243,271,467,411,607,439,523)(244,272,468,412,608,440,524)
> (245,273,469,413,609,441,525)(246,274,470,414,610,442,526)
> (247,275,471,415,611,443,527)(248,276,472,416,612,444,528)
> (249,277,473,417,613,445,529)(250,278,474,418,614,446,530)
> (251,279,475,419,615,447,531)(252,280,476,420,616,448,532), (  3,  4)
> (  5, 17,  7, 16,  8, 20,  6, 13)(  9, 19, 11, 14, 12, 18, 10, 15)
> ( 21, 23, 26, 28, 24, 22, 27, 25)( 31, 32)( 33, 45, 35, 44, 36, 48, 34,
>  41)( 37, 47, 39, 42, 40, 46, 38, 43)( 49, 51, 54, 56, 52, 50, 55, 53)
> ( 59, 60)( 61, 73, 63, 72, 64, 76, 62, 69)( 65, 75, 67, 70, 68, 74, 66,
>  71)( 77, 79, 82, 84, 80, 78, 83, 81)( 87, 88)( 89,101, 91,100, 92,104,
>  90, 97)( 93,103, 95, 98, 96,102, 94, 99)(105,107,110,112,108,106,111,
>  109)(115,116)(117,129,119,128,120,132,118,125)(121,131,123,126,124,
>  130,122,127)(133,135,138,140,136,134,139,137)(143,144)
> (145,157,147,156,148,160,146,153)(149,159,151,154,152,158,150,155)
> (161,163,166,168,164,162,167,165)(171,172)(173,185,175,184,176,188,174,
>  181)(177,187,179,182,180,186,178,183)(189,191,194,196,192,190,195,193)
> (199,200)(201,213,203,212,204,216,202,209)(205,215,207,210,208,214,206,
>  211)(217,219,222,224,220,218,223,221)(227,228)(229,241,231,240,232,
>  244,230,237)(233,243,235,238,236,242,234,239)(245,247,250,252,248,246,
>  251,249)(255,256)(257,269,259,268,260,272,258,265)(261,271,263,266,
>  264,270,262,267)(273,275,278,280,276,274,279,277)(283,284)
> (285,297,287,296,288,300,286,293)(289,299,291,294,292,298,290,295)
> (301,303,306,308,304,302,307,305)(311,312)(313,325,315,324,316,328,314,
>  321)(317,327,319,322,320,326,318,323)(329,331,334,336,332,330,335,333)
> (339,340)(341,353,343,352,344,356,342,349)(345,355,347,350,348,354,346,
>  351)(357,359,362,364,360,358,363,361)(367,368)(369,381,371,380,372,
>  384,370,377)(373,383,375,378,376,382,374,379)(385,387,390,392,388,386,
>  391,389)(395,396)(397,409,399,408,400,412,398,405)(401,411,403,406,
>  404,410,402,407)(413,415,418,420,416,414,419,417)(423,424)
> (425,437,427,436,428,440,426,433)(429,439,431,434,432,438,430,435)
> (441,443,446,448,444,442,447,445)(451,452)(453,465,455,464,456,468,454,
>  461)(457,467,459,462,460,466,458,463)(469,471,474,476,472,470,475,473)
> (479,480)(481,493,483,492,484,496,482,489)(485,495,487,490,488,494,486,
>  491)(497,499,502,504,500,498,503,501)(507,508)(509,521,511,520,512,
>  524,510,517)(513,523,515,518,516,522,514,519)(525,527,530,532,528,526,
>  531,529)(535,536)(537,549,539,548,540,552,538,545)(541,551,543,546,
>  544,550,542,547)(553,555,558,560,556,554,559,557)(563,564)
> (565,577,567,576,568,580,566,573)(569,579,571,574,572,578,570,575)
> (581,583,586,588,584,582,587,585)(591,592)(593,605,595,604,596,608,594,
>  601)(597,607,599,602,600,606,598,603)(609,611,614,616,612,610,615,613)
> (619,620)(621,633,623,632,624,636,622,629)(625,635,627,630,628,634,626,
>  631)(637,639,642,644,640,638,643,641)(647,648)(649,661,651,660,652,
>  664,650,657)(653,663,655,658,656,662,654,659)(665,667,670,672,668,666,
>  671,669)(675,676)(677,689,679,688,680,692,678,685)(681,691,683,686,
>  684,690,682,687)(693,695,698,700,696,694,699,697)(703,704)
> (705,717,707,716,708,720,706,713)(709,719,711,714,712,718,710,715)
> (721,723,726,728,724,722,727,725)(731,732)(733,745,735,744,736,748,734,
>  741)(737,747,739,742,740,746,738,743)(749,751,754,756,752,750,755,753)
> (759,760)(761,773,763,772,764,776,762,769)(765,775,767,770,768,774,766,
>  771)(777,779,782,784,780,778,783,781), ( 57, 85)( 58, 86)( 59, 87)
> ( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)
> ( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71, 99)( 72,100)( 73,101)
> ( 74,102)( 75,103)( 76,104)( 77,105)( 78,106)( 79,107)( 80,108)
> ( 81,109)( 82,110)( 83,111)( 84,112)(113,449,169,421,197,533,141,337)
> (114,450,170,422,198,534,142,338)(115,451,171,423,199,535,143,339)
> (116,452,172,424,200,536,144,340)(117,453,173,425,201,537,145,341)
> (118,454,174,426,202,538,146,342)(119,455,175,427,203,539,147,343)
> (120,456,176,428,204,540,148,344)(121,457,177,429,205,541,149,345)
> (122,458,178,430,206,542,150,346)(123,459,179,431,207,543,151,347)
> (124,460,180,432,208,544,152,348)(125,461,181,433,209,545,153,349)
> (126,462,182,434,210,546,154,350)(127,463,183,435,211,547,155,351)
> (128,464,184,436,212,548,156,352)(129,465,185,437,213,549,157,353)
> (130,466,186,438,214,550,158,354)(131,467,187,439,215,551,159,355)
> (132,468,188,440,216,552,160,356)(133,469,189,441,217,553,161,357)
> (134,470,190,442,218,554,162,358)(135,471,191,443,219,555,163,359)
> (136,472,192,444,220,556,164,360)(137,473,193,445,221,557,165,361)
> (138,474,194,446,222,558,166,362)(139,475,195,447,223,559,167,363)
> (140,476,196,448,224,560,168,364)(225,505,281,365,309,477,253,393)
> (226,506,282,366,310,478,254,394)(227,507,283,367,311,479,255,395)
> (228,508,284,368,312,480,256,396)(229,509,285,369,313,481,257,397)
> (230,510,286,370,314,482,258,398)(231,511,287,371,315,483,259,399)
> (232,512,288,372,316,484,260,400)(233,513,289,373,317,485,261,401)
> (234,514,290,374,318,486,262,402)(235,515,291,375,319,487,263,403)
> (236,516,292,376,320,488,264,404)(237,517,293,377,321,489,265,405)
> (238,518,294,378,322,490,266,406)(239,519,295,379,323,491,267,407)
> (240,520,296,380,324,492,268,408)(241,521,297,381,325,493,269,409)
> (242,522,298,382,326,494,270,410)(243,523,299,383,327,495,271,411)
> (244,524,300,384,328,496,272,412)(245,525,301,385,329,497,273,413)
> (246,526,302,386,330,498,274,414)(247,527,303,387,331,499,275,415)
> (248,528,304,388,332,500,276,416)(249,529,305,389,333,501,277,417)
> (250,530,306,390,334,502,278,418)(251,531,307,391,335,503,279,419)
> (252,532,308,392,336,504,280,420)(561,617,701,757,645,589,729,673)
> (562,618,702,758,646,590,730,674)(563,619,703,759,647,591,731,675)
> (564,620,704,760,648,592,732,676)(565,621,705,761,649,593,733,677)
> (566,622,706,762,650,594,734,678)(567,623,707,763,651,595,735,679)
> (568,624,708,764,652,596,736,680)(569,625,709,765,653,597,737,681)
> (570,626,710,766,654,598,738,682)(571,627,711,767,655,599,739,683)
> (572,628,712,768,656,600,740,684)(573,629,713,769,657,601,741,685)
> (574,630,714,770,658,602,742,686)(575,631,715,771,659,603,743,687)
> (576,632,716,772,660,604,744,688)(577,633,717,773,661,605,745,689)
> (578,634,718,774,662,606,746,690)(579,635,719,775,663,607,747,691)
> (580,636,720,776,664,608,748,692)(581,637,721,777,665,609,749,693)
> (582,638,722,778,666,610,750,694)(583,639,723,779,667,611,751,695)
> (584,640,724,780,668,612,752,696)(585,641,725,781,669,613,753,697)
> (586,642,726,782,670,614,754,698)(587,643,727,783,671,615,755,699)
> (588,644,728,784,672,616,756,700) );;
gap> CustomDisplayCompositionSeries( g );
Group
 | 2A(2,3) = U(3,3)
Group
 | 2A(2,3) = U(3,3)
Group
gap> List( ChiefSeriesOfGroup( g ), Size );
[ 36578304, 6048, 1 ]

# $A_5 \times A_5$ in primitive action on $60$ points
# (direct factors corresponding to left and right regular action)
gap> g:= AlternatingGroup( 5 );;
gap> e:= AsList( g );;
gap> gens:= GeneratorsOfGroup( g );;
gap> p:= List( gens, i -> PermList( List( e, j -> Position( e, i*j ) ) ) );;
gap> q:= List( gens, i -> PermList( List( e, j -> Position( e, j*i ) ) ) );;
gap> h:= Group( Concatenation( p, q ) );
<permutation group with 4 generators>
gap> IsPrimitive( h, [ 1 .. 60 ] );
true
gap> CompositionSeries( h );
[ <permutation group of size 3600 with 4 generators>, 
  <permutation group of size 60 with 2 generators>, Group(()) ]
gap> g:=PerfectGroup(IsPermGroup,10752,3);;
gap> g:=Group(GeneratorsOfGroup(g));;
gap> iso:=IsomorphismFpGroupByCompositionSeries(g);;
gap> iso:=IsomorphismFpGroup(g);;
gap> ImagesRepresentative(iso,Product(GeneratorsOfGroup(g)));
F3*F4*F5*F1*F2
gap> STOP_TEST( "grpprmcs.tst", 1);
